Getting Started Using Universal Mechanism
Contents
1. Pendulum model is also available at http www umlab ru download 50 eng pendulum zip Universal Mechanism 5 0 5 Getting Started 1 2 Model scheme Before modeling the pendulum with the help of UM we recommend to draw its sketch like you can see at the left As you can see we drew a simple pendulum and chose two systems of coordinates SC the base frame OX YoZo SCO and the body fixed frame SC1 The SCO origin is placed in the center of the joint the second one SC1 at the mass center of the pendulum The axes of SC1 are directed along the pendulum principle axes of inertia The base frame exists in every object and as a rule is connected with the Earth There is only rotational joint connecting the pendulum and the base frame the wall which the pendulum is attached to Universal Mechanism 5 0 6 Getting Started 1 3 Creating the model 1 3 1 Running UM Input and creating new model Running UM Input program 1 Click Start Programs Universal Mechanism 5 0 UM Input Creating a new model 1 From the File menu point to New object The window of the constructor appears see fig 2 1 3 2 Familiarizing yourself with Universal Mechanism Take a few minutes to familiarizing yourself with the Universal Mechanism constructor window see Figure 2 Tree of elements of a model in the left top corner of the constructor window is used for getting access to elements of the model Animation window in the center s2. Adding the joints with the External body is finished Universal Mechanism 5 0 50 Getting Started Connection points adding Connection points are necessary for the description of the connections We should add the points to the TLP_1 Pendulum3 and the TLP_2 Pendulum3 bo dies to describe the joints between the subsystems 14 Start edit of the TLP_3 subsystem select the subsystem from the compound object elements tree and click the Edit subsystem button 15 Point to the Bodies element of the subsystem object elements tree and select the Pendulum3 body 16 Come to the Points tab for the Pendulum3 and add a new point click the button A new point with zero coordinates in coordinate frame of the Pendu lum3 body will be added by default Coordinates of the point are shown in the table empty fields correspond to zero values Position of the point is marked on the image of the body The position of the point coincides with the position of the rotational axis between two pendulums x Name Pendulurrs aur ext a Oriented points Vectors Farameters Position Points EEr 2 MH ares a A Da Add point Ctrl SrayPlus f 17 Click the Accept button of the Close subsystem window The TLP_1 subsys tem will be closed NineLinkPend model will be activated 18 Add the connection point for the Pendulum3 body of the TLP_2 subsystem 19 Click the Accept button of the Close subsystem window The TLP_2 subsys tem will
3. Expression All forces Joint force wa Basel Coordinates Angular var Reaction F Linear war ey Pendulurn Bad Pendulum 0 T 0 Typ Resolved in SC of body SAE o bf CO eo C OMponer Ca C al2 lc x ey 2 A fr y Fendulum seg Coordinates of point 0 0 0 of body Pendulurr ryf Fendulurmn Universal Mechanism 5 0 27 Getting Started Let us draw a plot of Y coordinate of the mass center of the pendulum 3 Select Linear var tab linear variables coordinates velocities accelera tions etc 4 Select Y in the Component group 5 Then move the variable to the container with the help of the button v New variable r y Pendulum appears in the container of variables 6 Select the variable in the Wizard of variables and drag it to the graphical window 7 Select the Object simulation inspector and click the Integration button You can see the plot of your variable in the graphical window l Plots ale gai re Pendulum Animation of vectors and trajectories During the simulation you can animate various vector variables in an animation window Let us animate the vector of the mass center velocity Firstly we need to create such variable in the Wizard of variables Universal Mechanism 5 0 28 Getting Started 1 Select the Wizard of variables and there select the Linear var tab 2 Select v velocity in the Type group 3 Select V vector in the Component group 4 Add this
4. Hide Showy l Position b Saved plots can be loaded to any graphical window as static variables Plots of static variables will not be calculated again during simulation Universal Mechanism 5 0 48 Getting Started 1 5 2 3 Connections usage Previously we considered joints between the bodies of different subsystems of the compound model as the elements of the compound object Fig 1 7 scheme A page 33 Now we will use another approach We will describe kinematics of the multi body pendulum model with the help of connections Fig 1 7 scheme B page 33 Thereto we will make some changes in the subsystem models as well as the com pound model NineLinkPend Then we will simulate motion of the pendulum and compare the results with the previously saved ones Internal subsystem editing 1 Close simulation program UM Simulation and come back to the UM Input program 2 Point to the Subsystems element of the Ninelinkpend object elements tree Select the TLP_2 subsystem Par Es oOo Mame TLP_1 F ar 5 Type included y ent Edit subsystem General lo oe lor se d Open subsystem For editing 3 Click Edit subsystem button TLP_2 subsystem object will be opened in the UM Input program window One can edit the internal subsystem as an ordinary UM object but the corres pondent compound object is not available during this session Pay attention to the Close subsystem window in the top left corner of the screen
5. Universal Mechanism 5 0 74 Getting Started 9 Select the Initial conditions tab In the Coordinate 1 1 input 0 1 We need to shift the brick a bit because its position at zero coordinate 1s quite near to its equilibrium position that gives us small amplitude of oscillations if we do not shift the body Object simulation inspector Object variables kati Informatior Tools Solver Identifiers Initial conditions Coordinates Constraints for initials cp o P of ol Bo a bed Y Coordinate Meloy i Message d 0 1 z da 0 1 z Humber of d o f 1 Integration 10 Select the Solver tab Set Simulation time to 25 seconds 11 Run simulation clicking the Integration button Process of the numerical simulation starts for 25 seconds period You can see oscillations of the Brick in the animation window and time history of the vertical position of the brick Universal Mechanism 5 0 75 Getting Started 12 Click the 100 button in the drop down tool panel in the top or click the Show all menu command in the context menu see the Fig 2 9 Plot now fits the win dow l Plots alo Vanables rz Brick Co l Miana 3 3 Show all Show according the ruler pointers Copy to clipboard Print Fix tool panel 11 01 0 0117 Ex 1 Ey 1 Show ruler E Figure 2 9 Graphical windows after the first experiment Free oscillations without damping Now we will turn off damping and compare plot
6. puted The brick in the animation window is now in its equilibrium position Note Obtained coordinates which correspond to equilibrium position you can save to a file To do it use the h button in the Initial conditions tab This file with initial conditions you can loaded using Object simulation inspector in order to start simulation form the equilibrium position if necessary Natural frequencies and forms Select the Frequencies tab In the left list you can see the natural frequencies of the system As you can see our system has only one frequency and this frequen cy is 0 795775 Hz what corresponds to 5 0000 rad s Click the Show button to start animation of the natural forms Adjust appropri ate Amplitude and Rate Click the Stop button to finish animation Universal Mechanism 5 0 80 Stability Getting Started Let us find the roots of the linearized system It gives us the information about stability of the model 7 Set the Compute to Eigenvalues You can see that the real parts of roots are negative therefore system 1s stable Damping ratio 8 Let us describe the damping ratio of the system Click the right mouse button on the list of eigenvalues and from the context menu select the Frequen cy damping ratio menu command We have Beta 100 that corresponds to critical damping Linear analysis E4 Initial conditions Identifiers i E quilibriuirn Frequencies Compute Animation of m
7. 3 Run integration As we expected in the resonance case the amplitude of the os cillations increases in the long run see the Fig 2 14 l Plots alo vaot v rz Brnck Co i969 basz2 xed Eysi fA Figure 2 14 Forced oscillations resonance case Universal Mechanism 5 0 83 Getting Started 3 Subsequent studying Universal Mechanism You have come through two examples of dynamical systems pendulum and sprung body and have seen the basic tools and features of the UM Base version The Getting Started series includes other manuals that devoted to the rest mod ules of the Universal Mechanism Here they are e Getting Started simulation of road vehicles e Getting Started railway vehicle dynamics e Getting Started Matlab Simulink interface e Getting Started scanning and optimization module e Getting Started simulation of flexible bodies with UM FEM e Getting Started durability analysis Library of simple models how to The UM User s Manual includes 07_UM_Simulation_Examples pdf which is devoted to consideration of simple models that show you how to create model var ious graphical elements joints and force elements Studying these examples helps you familiarize yourself with basics of Universal Mechanism and approaches for simulation of objects of different kind The library of models is in the um_root samples library directory The 07_UM_Simulation_Examples pdf you can find in the um_root man
8. amp Odd from subsystems i Insert identifier shift Ins ma Edit identifier Delete identifier Del Copy value to clipboard Cbrl 0 Copy table to clipboard Ctrl Ins Show elements including identifier List of unused identifiers New sheet Rename tab Page identihier list Pelete tab Pelete sheet Universal Mechanism 5 0 70 Getting Started 4 Fill out the Add identifier form as it is shown in the figure below Hame kooo Expression egtem Comment Natural frequency men 5 Add one more identifier mu_star 2 sqrt c m It is a critical damping coef ficient Add identifier Name mu_star Expression 2 sqrt e m Comment Critical damping coefficient ores Universal Mechanism 5 0 71 Getting Started 2 3 8 Preparation for simulation 1 In the tree of elements select Object 2 Set Generation of equations to Numeric iterative see Inspector window in the right part of the constructor window 3 Save the model as Oscillator use menu command File Save as Now we will come to the simulation program 4 From the Object menu select Simulation or simply press F9 key The simulation programs starts and opens the current model Universal Mechanism 5 0 72 Getting Started 2 4 Simulation of motion Let us consider some particular cases of oscillations free damped oscillations and forced oscillations without damping 2 4 1 Free oscillations Free damped oscillations 1 Open new anim
9. set to zero That is why these bipolar forces will not influence on the dynamics of the model but give us a possibility to show the spring and the damper see the Fig 2 5 right lt 7 a lt zZ ar Figure 2 5 Visualization of forces Note There are several possible ways to describe elastic and damping forces in our model We used the way to describe them as joint forces but it 1s not the only right way We could introduce them as bipolar as well And in this latter case we would visualize them and introduce forces at once without intricate describing additional fake bipolar forces But such a way leads to a following problem Our ideal case that we consider here allows to model the situation when the length of the spring and damper equal to zero Imagine that the brick has so large amplitude that the attachment points of the spring and damper will be on the same level In such a case we have degeneration of bipolar forces that act along the line between the attachment points When we have zero length we could not find the direction of the bipolar forces Joint forces have no such a degeneration because they direction always coincide with the axis of the joint That is why we used very joint forces here Universal Mechanism 5 0 68 1 So select the Bipolar force in the tree of elements Getting Started 2 Add two bipolar force elements Set their parameters as it is shown in the Fig 2 6
10. After some modifications in the subsystem the user can confirm or cancel all changes in it as Close subsystem Close subsystem MERE Cancel Universal Mechanism 5 0 49 Getting Started Adding the joints with the External body Let us add to the subsystem TLP_2 the joint between the Pendulum and the External bodies 4 Point to the Joints element create new joint and rename it as jPendu lumi External 5 Select the Pendulum1 body in the Bodyl drop down list and the External body in the Body2 list as it is shown in the figure below 6 Change its Type to Rotational 7 Set 1 for the Z coordinate of the Body Body Body Pendulum External seen Pendulum ve Pendulurnz bean Pendulurn 8 Copy the jPenduluml_External to the clipboard main menu Edit Copy to clipboard see Fig 1 9 page 38 9 Click the Accept button of the Close subsystem window The TLP_2 subsys tem will be closed NineLinkPend model will be activated 10 Start edit of the TLP_3 subsystem select the subsystem from the compound object and click the Edit subsystem button 11 Paste the previously saved joint from the clipboard main menu Edit Paste The new element will appear on the Joints element of the subsystem elements tree 12 Point the new joint and select the Pendulum1 body as the Bodyl 13 Click the Accept button of the Close subsystem window The TLP_3 subsys tem will be closed NineLinkPend model will be activated
11. Object open dialog window will appear Press F5 key to refresh the list of files in current directory Select ThreeLink Pend_ Subs model and click OK Pare ES B Es x a Name TLP_1 ean oS Name LP_1 ary a Type Type none Type included Lom Type none Comments Text attribut 00 E estemal Edit subsystern H wheelset General Position Identifiers Identifier Show scene Open object Scan directory CAProgramn Files UM Software Labs A El CAProgram Files UM Software L H samples NineLinkPend Fa CAProgram Files UM Software Labyha Ki Cancel _ Universal Mechanism 5 0 40 Getting Started Setting of subsystem position Subsystem position is evaluated from kinematic constraints defined for its bo dies Nevertheless the user can preliminary set the position of subsystem in UM Input program for better visualization 4 Point to Position tab and set Z Translation to 1 as in the figure below pa Mame TLP_1 aT TT 5 Type mcluded bi ent ee Edit subsystem General Position Identifiers Translatio eooo g L eooo A 2a Rotation o 00000000 A jo 00000000 j jo 00000000 LA Translation after rotatia ANH 5 Copy TLP_1 subsystem two times 6 Rename new subsystems to TLP_2 TLP_3 7 Set Z Translation of TLP 2 to 4 and Z Translation of TLP 3 to 7 Subsystems are added Now we will create joints to d
12. be closed NineLinkPend model will be activated Subsystem editing is finished Universal Mechanism 5 0 D1 Getting Started Connections description 20 Point to the Connections element of the NineLinkPend object elements tree The element Connections is the list which contains all joints and force ele ments with the second body that is external In our case the list includes jPen dulum1_External joints of TLP_2 and TLP_3 subsystems X X C TLP_2jFPendulumi_Estermal El NineLink Ferd TLP_3jPendulunt External lag TLF 21 Double click on the box on the left of the element TLP_2 jPendulum1_External in the list Object tree will be opened where the lower level is the level of connection points 22 Select the point 0 0 0 of the Pendulum3 body of the TLP_1 subsystem The connection is ready 23 Double click on the box on the left of the element TLP_3 jPendulum1_External in the list 24 Select the point 0 0 0 of the Pendulum3 body of the TLP_2 subsystem The connection is ready Description of the connections is completed Deleting of the redundant joints The earlier created joints JTLP_12 and JTLP_23 of the compound object duplicate the joints described with the External body Let us delete them 25 Point to the Joints element of the NineLinkPend object elements tree 26 Delete the JTLP_12 and JTLP_23 joints i Mamelil LF_12 a ae z Body Body TLF_1 Pendulum3 Delete current elemen
13. eee E AN N E 72 Da DC ALIS OIC AE AINA SIG oo recserte A E E A setae 78 2 4 3 Lara S eE E E E A E EAEE 179 2 4 4 Forced oscillAONS acceso sescsisascnsatisscsinecomoaauncecanit ness ET i Sl 3 SUBSEQUENT STUDYING UNIVERSAL MECHANISM s asssnnnnnnnnnnnnnnnnnnnnnnnnnnn 83 Universal Mechanism 5 0 4 Getting Started 1 Model of a pendulum 1 1 What we will learn This lesson shows you how to create new model add rigid bodies and joints generate and compile equations of motion simulate dynamics of a model and ob tain plots of various performances of the model This lesson is devoted to general overview of the UM possibilities and workflow At the end of the lesson we will have the model of the pendulum you can find the final model in the um_root samples tutorial eng pendulum directory which will include one rigid body pendulum itself one rotational joint and graphical object of the environment support After describing the model we will go through the all stages of the working with the model synthesis and compiling of equations of motion and then will come to the simulation of motion of the pen dulum Support Pendulum Figure 1 Complete model Then we will create the model of the multi link pendulum by the development of the pendulum model and with the usage of the subsystem technique We will learn how to create compound models and features of working with mechanical systems with closed kinematical loops
14. of the va riables in text file with the help of the graphical window tools In our example we will use the both approaches We will compare simulation results for the models created according to the scheme A Fig 1 7 scheme A and the scheme B Fig 1 7 scheme B Creation of list of calculated variables 15 Activate the Object simulation inspector and point to the Object variables tab 16 Load the list of variables from file ninelinkpend var or just select all the variables from the Wizard of variables container and drag them to the white field of the tab 17 Turn on the Automatic saving of variables box Now the variables added to the tab will be automatically saved in the file of cal culated variables ninelinkpend tgr during simulation The directory of the object NineLinkPend will be used by default for the saving Object simulation inspector Solver Initial conditions Object variables matty Information Tools IW Automatic saving of variables L BG TER E Jninelinkpend No name my TLP_1 Pendu Coordinates of point 0 0 0 of bo mel TLF_1 Fendu Coordinates of point 00 0 of bo y TLF_1 Fendu Coordinates of point 0 0 0 of bo mel T LP 2 Pendu Coordinates of point 0 0 0 of bo my TL Po 2 Pendu Coordinates of point 0 0 0 of bo mel T LP 2 Pendu Coordinates of point 0 0 0 of bo mel TLF_3 Fendu Coordinates of point 0 0 0 of bo ey TLF_3 Fendu Coordinates of poi
15. Moder SC home aeara EE EEE EEEE EER 5 L3 Creatine the model 6 1 3 1 Running UM Input and creating new model sneesennsensseesssesssesssesseesssesssesssersserss 6 Lou Familiarizing yourself with Universal Mechanism ccccceesccceeeeeeeeeeeceneeseeenees 6 1 3 3 heal mS STA MICA OD CCS E E E E E E E E E E E 8 Je Pe Wo bo E EE eee ee ee ene eT 8 eee WMA SS Ol ie 0 UN e E E E E E E E E 14 1 3 4 Co A AN EDO ea ae sa sate ct cnr sind E E E E E 15 1 3 5 CG AGI YO TNS E E E E E EE E AE AA AN 16 1 3 6 SAITA NS TIN I EA E E E mvametineasinanamnacer 17 1 3 7 Preparation for simulation generation of equations Of motion s esseesssesseesse 18 1 3 7 1 Numeric iterative method secsnscccsaivarcscdinnnisiacdivwaasieosiancubinddnoncaddnoadcentiietwpndineedsiodieadas 19 Eo S a e O O en a E E E E TE E 20 1 3 8 Run UM Simulation Prostrani eeii eE aE EE EEEE 21 1 4 Simulation Of motion cccccccccccccccccccccccccccccccccscccceccecceccsccscescecccccccescescecceccocsccecees 22 15 IN UUPIOTIDO CY SUCTION oes cco aceceosesceencshacanesnonceasuscasts ce ssasennssnaceenetucennssneceanecncstecessestanseases 30 1 5 1 Development of the simple pendulum model c cc cecccceecccsesecceeeeeeeeeeeeeeeeeeeeens 30 L232 Usage of subsystem technique esiesieranseceouninsawanowientuamaaeaeaneneammesandnarsecnmaaeienatnsssmananes 32 L32 Compound objeci SUCHTE riasin ESR SEESE ENEE Oi 32 1 5 2 2 S bsystem preparation s
16. Nane P amp P os ext a Alec ME 2 Type amA Expression ll GU Spring Autodetection Attachment port Top Length Description of fore Pascal l expression F F f t Example cstiff e 0 cdiss y amplsin orm t Nare m et Me E 2 Type ami Expression G Damper Autodetection Attachment point Top Brick hk Length Description of fore Pascal C expression F F x vt Example cstiff 0 cdiss ampl sin orn t Figure 2 6 Fictitious bipolar forces Universal Mechanism 5 0 69 Getting Started 2 3 Additional parameters Using UM you can express one parameter via others Here we will add two new parameters in the model accurate analytical values of the natural frequency and the critical damping coefficient Our model is very simple that is why we can ob tain analytical solutions easily Natural frequency can be obtained according to the following formula k JE where m k natural frequency rad s c stiffness coefficient N m m mass of the body kg Critical damping coefficient can be found as u 24 cm where u critical damping coefficient Ns m n 3 Well add new identifiers parameters to our model Click the button in the list parameters or select the New identifier menu command from the context menu Sl Fea ees whole list Expression m 10 a 0 05 Fa _
17. Process parameters window will appear at the lower right corner of the screen faq Process parameters fo M Simulation time 6 62 W Duration time 5 829 MW Step duration 2 O 0011014 J Step size z 0 02 Pause a 4 At the end of the simulation the Pause window appears You can increase the simulation time change the numerical method etc Process parameters Solver statistics Simulation process parameters Solver options Type of solyvin C Aull Space Method f Range Space Method Simulation time fi 0 000 ta Step size for animation and data storage 0 02 Eror tolerance 1E 0005 Delay to real time simulation Continue Interrupt 2 Press the Interrupt button Object simulation inspector appears Universal Mechanism 5 0 26 Getting Started Drawing plots During the simulation you can see plots of various variables Such as velocities accelerations forces and so on We will open new graphical window create new variable to plot Y coordinate of the center of mass of the pendulum and draw its plot Well let us create new graphical window 1 From the Tools menu select Graphical window Open Wizard of variables 2 From the Tools menu select Wizard of variables The Wizard of variables is a special tool for creating variables which can be drawn in graphical windows or animated in animation windows in cases of vec tors or trajectories Efe Wizard of variables El pend User
18. Select the Geometry tab and set joint parameters as it is shown in the Fig 2 2 right e T at Top Oriented points Vectors i Type Z Translational aomen Description Joint force G i none o J AEE E a Jee 2 pec ame ass Figure 2 2 Creating translational joint Universal Mechanism 5 0 64 Getting Started 4 Point to Description tab 5 Turn on the Prescribed function of time check box 6 Set the Type of description to Expression and then input a sin omega t see the Fig 2 3 and press Enter E Namelio atat nz Body Body Basel Top Type Z Translational 7 Geometry Description Configuratio Rotation 0 000000000000 A Translation o 000000000000 A Joint coordinat Ie Prescribed function of time Type of descriptio Expression Time table C Function 0 File a sinlomega t t Figure 2 3 Prescribed function of time 7 In the Initialization of values window set a 0 05 m and omega 10 rad s Initialization of values Universal Mechanism 5 0 65 Getting Started Joint for the brick 1 Select the Brick body in the tree of elements 2 Click the E button 3 In the drop down list select Translational again 4 Select the Top as the first body instead Base see the figure below 5 Set the rest parameters of the joint as it is shown below NonefBak aas Body Body Top Brick Type Z Translational bd Geomet
19. Seta proper initial position of the chain with the help of the Initial condi tions tab Set 0 3 for all the model coordinates 12 Click Integration to run the simulation Mie x Animation window e A E e SS wes lw b Vectors Trajectories zan wo Pendulun velocity of pont 0 0 0 of body Pendulum relative to Basel SC Basel Vector w ty Fendulum Coordinates of point 0 0 0 of body Pendulum relative to Basel SC Basel Vector aa woy Pendulume Velocity of point 0 0 0 of body Pendulurie relative to Basel SC Basel Vector ad oyv Pendulume Coordinates of point 0 0 0 of body Pendulume relative to Basel SC Basel Vector re wo Pendulums Velocity of pant 0 0 0 of body Pendulum relative to Basel SC Basel Vector Universal Mechanism 5 0 32 Getting Started 1 5 2 Usage of subsystem technique Subsystem technique is used for creation of compound models of mechanical systems with the help of standard and user created subsystems Each subsystem is a mathematical model of the part of the mechanism We will add the model of three link pendulum TLP ThreeLinkPendulum three times as subsystems to a new object to create a nine link pendulum model Creation of compound objects from included subsystems is considered in this section 1 5 2 1 Compound object structure To create the compound model of multi link pendulum we should define its structure and way of description of interaction between s
20. Started Universal Mechanism 5 0 14 Getting Started 1 3 3 2 Image of pendulum 1 Return to the Images item in the Inspector 2 Create new graphical object 3 Rename new graphical object to Pendulum Note Do not forget to press Enter after any modification of the text data in order to reflect this The pendulum image consists of two graphical elements an ellipsoid and a cone 4 Add new graphical element Ellipsoid and set its parameters a 0 05 b 0 2 c 0 2 Set diffuse color to blue 5 Add new graphical element Cone and set its parameters R2 0 03 R1 0 03 h 1 Set diffuse color to blue Now image of the pendulum is ready Universal Mechanism 5 0 15 Getting Started 1 3 4 Creating rigid bodies The pendulum as a mechanical system consists of the only body Point to the Bodies item in the Inspector Create new body Rename body to Pendulum Select Pendulum from the drop down list Image ee os YY Ff Set Mass 1 kg x Name Egu ext a Oriented points Vectors Parameters Position Paints Go to element hee Image M Visible Pendulum Compute automatic Inertia parameter Mass Inertia tensor Coordinates of center of mas 7 4 Universal Mechanism 5 0 16 Getting Started 1 3 5 Creating joints The rotational joint connects the Pendulum and the BaseQ To create new joint do the following actions 1 Point to Bodies Pendulum 2 Click the button A
21. Universal Mechanism 5 0 1 Getting Started Getting Started Using Universal Mechanism This manual leads you through the basic possibilities of Universal Mechanism software and shows you how to create and simulate models of several simple me chanical systems It assumes that you go through the manual step by step sequen tially Simulation of such mechanical systems as cars and railway vehicles has certain ly its own features but basic concepts using UM still the same These concepts are shown in this manual Copyright and trademarks This manual is prepared for informational use only may be revised from time to time No responsibility or liability for any errors that may appear in this document is Supposed Copyright 2009 Universal Mechanism Software Lab All rights reserved All trademarks are the property of their respective owners Contact information The latest UM version as well as up to date UM user s manual available at http www umlab ru download htm Please send your bug reports questions and suggestions to um umlab ru Address Russia 241035 Bryansk bulv 50 let Oktyabrya 7 Bryansk State Technical University Laboratory of Computational Mechanics Prof Dmitry Pogorelov Phone fax 7 4832 568637 Universal Mechanism 5 0 2 Getting Started 1 MODEL OF A PENDULUM 0 cece cece eee ce cee e eee e cece ce eeeeeeeeeseseseeeeeeeeseeeseeeeeeeeees 4 LLE Wia WS whi eaire NEEE ENEE EAEE EEE ENERE 4 L
22. ars 2 Select Compile equations 3 Click Generate button If generating and compiling equations of motions end successfully yov ll see the message box Compiling successful Object is ready for simulation The model is ready to be loaded in the UM Simulation program 1 3 8 Run UM Simulation program 1 Select Object Simulation menu item UM Simulation program starts and opens the current model Universal Mechanism 5 0 22 Getting Started 1 4 Simulation of motion Now we are in the simulation program We will open new animation window deflect the pendulum from vertical position to 1 radian and run simulation of dy namics of pendulum Creating new animation window 1 From the Tools menu select Animation window New animation window appears Familiarize yourself a bit with an animation window Rotating Point the mouse cursor to the animation window so that cursor looks like the picture in the figure to the right Press left mouse button and rotate the Sins model in the animation window Shifting Point the mouse cursor to the animation window so that it has Rotating shape press Ctrl key and mouse cursor changes to Shifting mode Press left oy mouse button and shift model in the animation window Zoom in zoom out Point the mouse cursor to the animation window and press Shift key and with the help of left mouse button zoom in out the model You can also use a mouse scroll wheel After some practice you ca
23. ation window Tools Animation window Open new graphical window where we will plot time history of the vertical po sition of the brick 2 Open new graphical window Tools Graphical window Open Wizard of variables Tools Wizard of variables Select the Linear var linear variables tab select Brick in the list of bodies e U set Type to r coordinate set Component to Z Click the v button to create new variable The variable appears in the container of variables Drag the varia ble to the graphical window Close the Wizard of variables 5 From menu Analysis select Simulation The Object simulation inspector ap pears 6 Arrange windows on the desktop as you prefer for example as it is shown in the Fig 2 7 lept b DOSE ESETB TO Se oF hee ua eer r es a es e o ete a aa a Integration Figure 2 7 Desktop of the simulation program Universal Mechanism 5 0 73 Getting Started 7 Select the Object simulation inspector and click the Identifiers tab 8 Set a to 0 and press Enter So we set zero amplitude of the oscillations of the Top body in other words we fix the Top in order to analyze free oscillations Object simulation inspector Object variables PE Information Tools Solver Identifiers Initial conditions S fd whole ist Name Expression Value Comme mi 10 10 250 0 4 5 sort cy m mustar 2 sqrt c m Integration Figure 2 8 Parameters of the model
24. bject Set its name to Spring Add new graphical element Spring Set Spring parameters as it is shown below X Nane e AS ext Description Go position Spring Type EE Spring PRP AP et ed GE position Maternal Parameters Color C Left Right fadus eigh d bar 0 02 C Number of coils 5 pA Coil discretization 20 pA Bar discretization i 0 pA Getting Started Universal Mechanism 5 0 60 Getting Started A WO N e Damper Now we come to the last graphical object in this model damper Create new graphical object Set its name to Damper Add new graphical element for the Damper Cone Set parameters as follows R2 0 02 R1 0 02 h 1 Select the Color tab and choose blue for diffuse and specular colors 6 Add one more Cone with the following parameters R2 0 04 R1 0 04 h 0 5 In the GE Position tab set Translation Z to 0 25 Select red diffuse and specular colors Universal Mechanism 5 0 61 Getting Started oe fe a 2 3 3 Creating rigid bodies Top Create new rigid body Top Add new rigid body Set its name to Top In the Image list select Top Leave Mass and Inertia tensor empty Top Hame Top 4h t aa Onented points Vectors Parameters Points To element S Image none Coordinates of center of mas Universal Mechanism 5 0 62 Getting Started Brick Now we will create one more rigid
25. body Brick Its mass we will express via parameter identifier m Such a parameterization gives us a possibility to change its mass easily and quickly obtain results for various values of the mass of the brick without regeneration equations of motion Otherwise we would have to gen erate equations every time we want to change its mass Add new rigid body Rename it to Brick In the Image list select Brick Set Mass to m and press Enter New Initialization of values window appears Set Value to 10 Press Enter This new parameter appears in the parameter list in the bottom left corner of the Nm PWN constructor window see the figure below st xj Initialization of valu es ne ak 8 BE Oriented points Vectors Parametere Posion Points Add to the sheet Go to element EA Image Iv Visible Brick E xj Whole list m 10 Universal Mechanism 5 0 63 Getting Started 2 3 4 Creating joints Joint for the top The Top body moves along the vertical direction according A sin w t function Now we will describe the translational joint between the base and the top and set the coordinate in this joint as a time function 1 Select the Top body in the tree of elements 2 Click the button Select Create joint and in the drop down list select Trans lational see the Fig 2 2 left The new joint of this type is created Now you can see parameters of the joint 3
26. cally from the plot of the power spectral density see the Fig 2 12 It is approximately 0 78 Hz see abscissa in the left bottom corner 0 78 Hz gives us 0 78 27 4 9 rad s You can see that numerically obtained values are quite close to analytical one Note To pick the frequency more precisely use changing scale of the window as it is shown in the Fig 2 12 ne Statistics spectral estimations Histograrn Integral law Correlation function rz Brick Co Power spectral density Spectrum module Spectrum phase Statistics 0 779 0 01042 aa aa aaa 7 Figure 2 12 Power spectral density of the free oscillations Universal Mechanism 5 0 79 Getting Started 2 4 3 Linear analysis Let us consider an example of using the Linear analysis With the help of this tool we will find the equilibrium position of the system its natural frequencies and forms define how much the actual damping ration relative to the critical one Well at first you need to close Pause and Object simulation inspector win dows l A Select the Pause windows and click Interrupt Select the Object simulation inspector and click Close Open Linear analysis window From the Analysis menu select Linear analysis The Linear analysis window appears Equilibrium position In the Linear analysis window select the Equilibrium tab Click the Compute button You can see the message Equilibrium position is successfully com
27. djust joint and select Rotational joint in the context menu After that the rotational joint is created and named as jPendulum automatical ly Joint points and joint vectors describe the position of the rotation axis relative to each of the bodies Their coordinates must be given in the corresponding body fixed systems of coordinates 3 In the group Joint points Pendulum set Z position to 1 So the pendulum will swing around its upper point o Body Bade Geometry Description Joint forge Basel j AE T Pendulum i E a Universal Mechanism 5 0 17 Getting Started 1 3 6 Saving the model Now your model is described completely And it is high time to save it Let the object name be Pendulum 1 Select menu item File Save as 2 Set Path to UM Path Pend in the way how it is shown in the figure be low Save as Path including abject name C Program Files UM Software Labs UMSO Fer l arcel Universal Mechanism 5 0 18 Getting Started 1 3 7 Preparation for simulation generation of equations of motion Program package Universal Mechanism UM consists of two programs UM Input program UMInput exe and UM Simulation program UMSimul exe Now we should prepare our model for subsequent analysis in the UM Simula tion program We should choose the method of generation of equations of motion Universal Mechanism supports two methods symbolic and numeric iterative Let us co
28. e it as JTLP_12 6 Select the TLP_1 Pendulum3 as Bodyl and the TLP_2 Pendulum1 as Body2 for the JTLP_12 joint 7 Set Type for the joint Rotational 8 In the group Joint points Pendulum1 set Z position to 1 Creating joint between the TLP_2 and TLP_3 subsystems 9 Copy the JTLP_12 joint as JTLP_23 10 Select the TLP_2 Pendulum3 as Bodyl and the TLP_3 Pendulum 1 as Body2 for the JTLP_12 joint 11 Set Type for the joint Rotational 12 Inthe group Joint points Pendulum1 set Z position to 1 13 Save the model NineLinkPend By default the numerical iterative method of generation of equations of motion is used Sect 1 3 7 1 page 19 Compound model description is now finished Now it corresponds to scheme A see Fig 1 7 page 33 Let s start simulation and save some results Universal Mechanism 5 0 1 5 2 2 Preparation for simulation Simulation 1 Run UM Simulation Object Simulation 2 Open the Object simulation inspector Analysis Simulation 3 Point to the Initial conditions Coordinates tab and set 0 1 value for all model coordinates Pay attention to the marked strings of the coordinate table These strings cor respond to coordinates of the cut joints three coordinates of the jPendulum1 joint in each of the subsystems Coordinates in cut joints are dependent and are calculated based on values of independent coordinates Initial values of these coordinates cannot be set by
29. e to Basel SC Basel projection r cyTLP1 Pendulums Coordinates of point 0 0 0 of body TLP_1 Pendulums relative to Basel SC Basel projection r ry TLF_2 Pendulum Coordinates of point 0 0 0 of body TLP_2 Pendulum relative to Basel SC Basel projection r cy TLP 2 Pendulum Coordinates of point 0 0 0 of body TLP_ 2 Pendulume relative to Basel SC Basel projection r my TLP2 Pendulum3 Coordinates of point 0 0 0 of body TLP_2 Pendulum relative to Basel SC Basel projection r ry TLFP_3 Pendulum Coordinates of point 0 0 0 of body TLP3 Pendulumd relative to Basel SC Basel projection r y TLF_3 Pendulum Coordinates of point 0 0 0 of body TLP_3 Pendulum relative to Basel SC Basel projection r cy LP S Pendulum3 Coordinates of point 0 0 0 of body TLP_ 3 Pendulum relative to Basel SC Basel projection r 12 Save the list of variables as ninelinkpend var use the a button from the top panel of the window The directory of the object NineLinkPend will be used by default for the saving Drawing plots Let us create new graphical window 13 From the Tools menu select Graphical window 14 Select all the variables from the List of variables window and drag them to the graphical window Universal Mechanism 5 0 46 Getting Started Saving results Simulation results time histories of the variables can be saved as the file of calculated variables tgr From the other hand the user can save plots
30. eate new graphical object Set its name to Top Add new graphical element Box Set parameters and GE position for the Box as it is shown below Select the Color tab and choose blue for diffuse and specular colors ee aS Wamel RAPE Name Ton ____ 6 fh ent C Text Description Go position Description Go position Box Box Ipe Bo AAE ef EE C Text pem Text i GE position Material Parameters Color Parameters Color GE position hd aterial A ile C B 2 C C 10 01 C Discretization E LA Universal Mechanism 5 0 58 Getting Started Brick Let us describe the brick as a cube of 0 2 m side length Create new graphical object Set its name to Brick Add new graphical element Box into this graphical object Set its parameters and GE position ae eS Select the Color tab and set red for diffuse and specular colors X X ep ERE nepa o e 2888 ext C Test Description Go position Description GO position Box Box Type OF Box AP AE An TypeA Bow zl cet Ee r ext ext a i GE position Material Parameters Color Parameters Color GE position Material a D2 C Translatio B 02 T p en Discretization o pA o e rE pi T i D o e MJ Universal Mechanism 5 0 59 a ae ee Spring Now we will create the graphical object for the spring Create new graphical o
31. escribe interaction be tween the subsystems into nine body pendulum model Universal Mechanism 5 0 41 Getting Started 1 5 2 1 3 Creating joints NineLinkPend now includes three subsystems Each subsystem contains three simple pendulums connected in series with rotational joints with d o f To create nine body pendulum kinematics we should set rotational joints of the pendulum support and rotational joints between the subsystems 1 Come to Joints element in the tree of elements Creating pendulum support joint The rotational joint connects the Pendulum and the BaseQ To create new joint do the following actions 1 Create a new joint Let the joint name be jSupport 2 Select the Base as Body1 and the TLP_1 Pendulum1 as Body2 X x Name Suppot a AP AS Name iSuppot a AP AS Body T Body Body Basel TLP_1 Pendulumi1 Ral Basel TLP_1 Perndulurrr NineLink Ferd Type Type F o Type e Rotational Aa External Geometry Description Joint force Bi ve Pendulume dh Pendulum gg TLP_2 ga TLPS Pendulurn1 R O Y T Joint vector Basel axis 2 0 0 0 Pendulurn axis 2 10 0 3 Set Type for the joint Rotational 4 In the group Joint points Pendulum1 set Z position to 1 So the pendulum will swing around its upper point Universal Mechanism 5 0 42 Getting Started Creating joint between the TLP_1 and TLP_2 subsystems 5 Copy the jSupport joint and renam
32. eseris E E A 34 1 5 2 1 Compound model creation ice ccdsoscapstadawdeetijasnapetecaedeetvesaepedeceodestvesenpetdaneest vases 37 ec 2M WN a bom EA YeE dee 721516 Pe nee hee eee een ee E ene tee eee 37 1 3 2 1 2 UD SV SUS SCO secare E EEE E vamunaanaeaenees 39 Ze KM RCATIIE TO MMLS a ieaesaen ase sie nes E E 41 F322 SMU eriein EIEEE EAEE EEEE ETE ASEET 43 Loa LOO S E an E E A 48 2 FREE AND FORCED OSCILLATIONS oo cccccceceeseceseceeceseeeuseecuseeeuseeenseeeaneens 55 2 1 What we will learn so0eoe0e0sosososososcsesesessssosososososeossessssssssosososeosssosssosssosososessossssso 55 22e Moncler he MOs 55 Dede Cream hE TINO CON gases sccsceces ccansnsccsatcescpetsesseesseanesdonseus consbowssdenssss csashonsscoaesesceasaseccsesece 56 2 3 1 Running UM Input and creating new model nnnssenssesseessensserssersserssersssrsssesse 56 2252 PATI GEA MICA OC CON cape descent seer cesna captor E 57 Dd CT ANTS riod DOUES cesena nara manne E EER 6l 2 3 4 PC ANS O E E A E A 63 2 9 9 Rea TORCE Cle NCIS e E E ot ieee tet naria 66 2 3 0 Visualization of spring and damMpet ccceccccsecccnescceeecceeeseceeeceeaeseeseneeeenseeseseees 67 aefa AON al E e E E E E 69 2 3 8 Preparation Tor Sinul esee nnen EEEE 71 Universal Mechanism 5 0 3 Getting Started 2 4 Simulation Of MOTION cccccccccccccccsccccccccccccccsccccecceccccceccsceccesceccccsccescescesceccccsscsscess 72 2 4 1 Je oa 6 Gl 1516 E E EE
33. f body TLP_2 Pendulum relative to Basel SC Basel projection r p TLP_3 Pendulum Coordinates of point 0 0 01 of body TLP_3 PFendulum relative to Basel SC Basel projection r y TLF_3 Pendulum Coordinates of pomt 0 0 0 of body TLP_3 Pendulum relative to Basel SC Basel projection r ey TLF_3 Pendulumd Coordinates of pomt 0 0 0 of body TLFP_3 Pendulum relative to Basel SC Basel projection r 32 Drag the two last variables from the ninelinkpend var list of variables win dow to the new graphical window The plots of the variables will be calculated during simulation 33 Use Tools List of calculated variables to load the file of calculated va riables ninelinkpend tgr E ninelinkpend tgr list of variables aae Ho name Comment y TLP_1 PFendulum Coordinates of point 0 0 01 of body TLP_1 Fendulum relative to Basel SC Basel projection r y TLF_1 Pendulum Coordinates of pomt 0 0 0 of body TLP_1 Pendulum relative to Basel SC Basel projection r p TLP_1 Penduluma Coordinates of point 0 0 01 of body TLP_ 1 Pendulum relative to Basel SC Basel projection r my TLP 2 Pendulum Coordinates of pomt 0 0 0 of body TLP 2 Pendulun relative to Basel SC Basel projection r mel T LP 2 Pendulum Coordinates of point 0 0 01 of body TLR 2 Pendulum relative to Basel SC Basel projection r my TLP 2 Pendulums Coordinates of pomt 0 0 0 of body TLP_ 2 Pendulum relative to Basel SC Basel
34. hows the model or its elements A frame is shown in the center of animation window There is the following identification for axes Red X Green Y Blue Z RGB Point of view zoom and other settings can be changed via toolbar buttons Using the context menu you can set perspec tive parameters supporting grid etc Inspector at the right hand side of the constructor is the main tool for the de scription of elements It shows parameters of an active element It contains full in formation about current element of the model Universal Mechanism 5 0 7 Getting Started age mepa g mai u Ec i Piz F Hp tl ARENE Hi Figure 2 Constructor window Universal Mechanism 5 0 8 Getting Started 1 3 3 Creating graphical objects We recommend to start describing any mechanical system with creating a set of graphical objects GO of the elements of the model 1 3 3 1 Scene image Creating new graphical object scene Scene is a graphical object corresponding to fixed elements of the object De scribing the scene is optional To create a scene you should make a usual graphical object and assign it to the scene image As for our example it 1s an image of the fixed joint where the pendulum is attached to support In order to create the cor responding image you should do the following steps 1 Point to Images element of Tree of elements 2 Click 2 button in the top of the Inspector to create new graphical object
35. ic iterative method does not suppose explicit steps of generation and compilation of equations of motion and seems to be simpler in usage Recommendations For beginner users it is strongly recommended to use the numeric iterative me thod of generation of equations of motion as simpler in usage The symbolic me thod might be recommended for more experienced users which work with more or less complex models During the Getting Started series we will use the numeric iterative method as the basic one Chapters 1 3 7 1 and 1 3 7 2 contain the descriptions of preparing for simulation sequence in case of usage of the numeric iterative and symbolic methods of gener ation of equations of motion consequently 1 3 7 1 Numeric iterative method 1 In the tree of elements select Object 2 Set Generation of equations to Numeric iterative see Inspector window in the right part of the constructor window 3 Save the model again Now the model is ready for simulation within the UM Simulation program How to start numerical simulation please read in the Sect 1 3 8 Run UM Simula tion program page 21 Universal Mechanism 5 0 20 Getting Started 1 3 7 2 Symbolic method If you used the numeric iterative method for generation of equations of motion you may omit this section and come directly to Sect 1 3 8 The UM Input is used for creating objects generating their equations and com piling them with the help of an external compile
36. int to the Color tab and set diffuse color to red Universal Mechanism 5 0 11 Getting Started Creating new graphical element cone 1 Create new graphical element and set its type to Cone Note Do not add new graphical object instead new graphical element within graphical object In this example we create the only graph ob ject Support which contains three graphical elements sphere cone and box 2 Point to Parameters tab and set R2 0 1 R1 0 h 0 15 3 Set diffuse color to red Universal Mechanism 5 0 12 Getting Started Creating new graphical element box 1 Create new graphical element and set its type to Box 2 Point to Parameters tab and set A 0 5 B 0 5 C 0 05 3 Point to GE Position tab Set Translation Z to 0 15 see Figure 6 lanea e hh ae ext Description GO position Elipsoid Cone Box oE Box e Pe ao ent Ee Parameters Color GE position Material Figure 6 Graphical element position Universal Mechanism 5 0 13 Assigning Support as scene image 1 Point to Object item of Tree of elements 2 Select Support in the Scene image list a Sensors LSC Variables Curves Object Options Path C Progran FilesSUM Software Lab4uh Object typ General Rail vehicle Equation generatio C Symbolic f Aumeric lterative Direction of gravit Characteristic size i 00 pA Scene image Support Getting
37. ion of joints between them will result in creation of several closed kinematics loops in model kinematics graph In other words the number of model joint coordinates will be grater then the number of de grees of freedom of the multi body system To remove closed kinematics loops we should cut a few joints The number of joints to cut equals that of independent cycles in the graph As soon as the automat ic choice of such joints is ambiguous and can result in non optimal model perfor mance the user has an ability to select by himself Coordinates of the rotational joints between the bodies are the most suitable for the description of the multi level pendulum model Therefore we should select Weight value for the joints connecting the first body of each of the subsystems with the BaseO in a special way to explain program that we want to cut them Universal Mechanism 5 0 36 Getting Started 5 Click to show hide a panel of addition joint data Name Penditm a HP ar i Shaw additional data Type ss J Edot Geometry Coordinates Translational degrees of freedom 0 000000000000 LA jw r 0 000000000000 2 W z 0 000000000000 A Rotational degrees of freedom Onientation angles A a C 2 aooocccooo00 BI C a pooo 4 X Name Pendulum aF apr j Comments T ext attribute We Convert to generalized Weight 1000 NDOF 3 gt In tree T oo ea a Geometry Coordinates Translati
38. ional joint JPendulum in ThreeLinkPend model with 3 degree of freedom joint that permits planar motion of mechanical system in oscillation plane 1 Close the UM Simulation program and come back to the UM Input program The ThreeLinkPend model is available 2 Come to Joints element in the element tree and select JPendulum joint jPendulum joint describes rotational degree of freedom between basic body Base0 and Pendulum body pu UI Object ThreeLinkPend sid UI Object ThreeLinkPend sid El Object a Object i Subsystems Images l i Bodies El Joints 2 E oon Pendulum so Pendulum Universal Mechanism 5 0 35 Getting Started 3 Change Type of the joint to 6 degree of freedom joint X X Name Perdim Jata ay Name Perdaun Jate z Body Body Body Body Basel Pendulum Pendulum Type B Rotational Type 9 E d a f Rotational Geomety Coordinates Ee Translational Translational i TL Generalized degrees of freedom 2 Quatemion C x acoooocooca00 JA jw Y o c00000000000 A lw z o 000000000000 A ai nan Rotational seo degrees of freedom T T T tienen oneles axis o 1 0 0 Cardan 1 2 3 2 Cs B L 2 pooooooooomo 4 F a A 4 Switch off 3 degrees of freedoms as shown at the left figure Now Pendulum Pendulum2 and Pendulum3 can fulfill planar motion in oscillation plane Joints cutting settings Adding of the subsystems and descript
39. ism 5 0 55 Getting Started 2 Free and forced oscillations 2 1 What we will learn In this lesson we will learn how to add forces preset movement of a body as a time function and use parameterization of a model We will use Linear analysis for obtaining the equilibrium position of a system natural frequencies and forms As well as we will analyze the spectrum of output data using the Statistics tool 2 2 Model scheme The example of simulation of free and forced damped oscillations is considered In this lesson we will create the model shown in the Fig 2 1 Model consists of two rigid bodies Top and Brick two translational joints a linear spring and a damper We will set vertical coordinate of the upper body as a sinusoid function You can find the final model in the um_root samples tutorial oscillator di rectory or download it using the following link http www umlab ru download 50 oscillator zip Asin t Brick Figure 2 1 Model scheme Universal Mechanism 5 0 56 Getting Started 2 3 Creating the model 2 3 1 Running UM Input and creating new model Running UM Input program 1 Click Start Programs Universal Mechanism 5 0 UM Input Creating a new model 1 From the File menu point to New object The window of the constructor ap pears Universal Mechanism 5 0 57 Getting Started 2 3 2 Creating graphical objects Top We will create a thin rectangular plate as a graphical object for the Top body Cr
40. n get something like shown in the figure below afin boy erin Deme trut Pelee L Universal Mechanism 5 0 23 Start simulation 1 From the Analysis menu select Simulation Window of the Object simulation inspector appears Object simulation inspector EEE LE Getting Started Universal Mechanism 5 0 24 Getting Started Initial conditions You should deflect the pendulum a bit in order to obtain its motion There ex ists a special tool for this purpose a wizard of the initial conditions 1 Select the Initial conditions Coordinates tab You can see a complete list of the object coordinates In our case there is only one coordinate in JPendulum joint 2 Set Coordinate to 1 Press Enter key Your pendulum has deflected Note Universal Mechanism uses System International SI Angular values have dimensions of radian me Animation window ila Object simulation inspector E mf m oe E afte Pe a TS Object variables Mh Information SS SSS ee SESS ees Solver Initial conditions a Cy ig Ef H Coordinates Constraints for initials fh o lt 0 8 oe oe fhe Coordinate Velocity l 0 Message d 0 1 y da 0 1 y Humber of d o f 1 Integration Universal Mechanism 5 0 25 Getting Started Simulation Now your model is ready for simulation Simply start simulation process for the 10 seconds 1 Click Integration button in the Object simulation inspector
41. ndulum Sa cut 0 1 U TLP_1 jPendulume 1a 0 1 T TLFP_1 Penduluma 1a 0 983441 296 0 TLFP_2 Fendulum clcut 3 851 46622 0 TLP 2 Pendulum 2cfcut 0 4 U TLP_2 Pendulum Jal cut 0 1 0 TLF_ 2 Fendulumz 1a 0 1 0 TLF_ 2Fenduluma 14 0 1 0 TLP 2 Pendulum External 1a 267172699 0 TLP_3 Pendulum clcut 5 31 922859 0 TLP_3 Pendulum 2c cut 0 7 T TLP_ Pendulum Sal cut 0 1 T TLP _3 Pendulum 1a 0 1 T TLP_ Pendulum 1a 0 1 U TLP_ 3 Pendulum External 1a Message dx 0 1 ia da 0 1 Number of dof 9 Integration Universal Mechanism 5 0 53 Getting Started 30 Create a new graphical window Tools Graphical window 31 Create a new List of variables window Tools List of variables and load file ninelinkpend var ninelinkpend var list of variables d f i Ho name Comment u TLF_1 PFendulum Coordinates of pomt 0 0 0 of body TLP_1 Pendulun relative to Basel SC Basel projection r y TLFP_1 Fendulum Coordinates of point 0 0 0 of body TLP_1 Pendulum relative to Basel SC Basel projection r ey TLF_1 Penduluma Coordinates of pomt 0 0 0 of body TLP_1 Pendulum relative to Basel SC Basel projection r p TLP_2 Pendulum Coordinates of point 0 0 01 of body TLP_2 FPendulum relative to Basel SC Basel projection r y TLF_2 Pendulum Coordinates of point 0 0 0 of body TLP 2 Pendulum relative to Basel SC Basel projection r ey TLF_2 Penduluma Coordinates of pomt 0 0 0 o
42. nsider them more detailed Symbolic generation of equations of motion Symbolic method assumes generation equations of motion as source files in C or Pascal with posterior their compilation by one of the supported external compi lers As a result of compilation the UMTask dll appears This dll is used by UM Simulation program for numerical integration of equations of motion Generation and compilation of equations of motions are performed within UM Input program Numeric iterative generation of equations of motion Numeric iterative method assumes generation of equations of motion on each step of numerical integration directly in UM Simulation program Comparison of symbolic and numeric iterative methods Let us consider advantages and disadvantages of both methods In terms of CPU efforts the symbolic method is faster It provides decreasing CPU efforts up to 10 30 for complex more than 10 20 degrees of freedom models For rather simple models CPU efforts for both methods are roughly the same The symbolic method during generation of source code fulfils its optimiza tion from the point of view of CPU efforts On the other hand the symbolic method of generation of equations of motion expects any external compiler to be installed on the same computer Universal Me chanism supports Borland Delphi Borland C Builder Microsoft Visual C as external compilers Universal Mechanism 5 0 19 Getting Started At the same time the numer
43. nt 0 0 0 of bo my TLF_3 Fendu Coordinates of point 00 0 of bo Integration Universal Mechanism 5 0 47 Getting Started Simulation Let us simulate 30 second of motion of the multilink pendulum 18 Point to the Solver Simulation process parameters tab of the Object inspec tor wizard and set 30 in Simulation time field 19 Click Integration button to start simulation One can minimize animation win dow to make simulation faster You can see the plot of your variables in the graphical window Saving plots in text files 20 Point to the graphical window Then select the two last variables in the list of variables of the window and click on the right mouse bottom The popup menu will be opened Select the Save as text file tool from the menu and save the plots to result txt text file The directory of the object NineLinkPend will be used by default for the saving l Plots lel Es Variables B TLP 1 Pen 04 B iiTLP_1 Pen B iiTLP_1 Pen B TLP 2 Pen B TLP 2 Pen B TLP_2 Pen My Tle 3 Pen a iv Options yi I 3 Y Edit Lad 2 Delete i y Copy to clipboard y y Copy to active MS Excel book Ctri E T a ele nea ace aa iain aed dete ee Filter Ctrl F Copy as static variables Ctrl 5 F Save as text file Save as tor File Ctrl Read From text File Read from RSP File Lay off variable as abscissa Lay off time as abscissa Clear Ctrl Del Select all Ctrl 4
44. odes Natural frequencies Hz f Eigenvalues ae ae Bo A 2 0 000331041 100 Save to file Copy to clipboard w Frequency damping ratio Lut Dema ee IT oo o Animate Note Damping ration shows us if all forms are damped properly and thus change damping coefficients or geometry of attachment point of dam pers if necessary 9 You can change the value of the mu identifier in the Identifiers tab and see what will happen with damping ratio 10 Close the Linear analysis window Universal Mechanism 5 0 81 Getting Started 2 4 4 Forced oscillations Let us consider simulation of forced oscillations without damping 1 Delete all variables from the graphical window except the first dynamic one 2 From the Analysis menu select Simulation 3 Select the Identifiers tab Set the following values a 0 05 omega 8 mu 0 4 Run integration Now you can see that the body Top also moves The time his tory of the vertical position of the Brick is given in the Fig 2 13 l Plots Pile Es Variables W r 2 B rick To Pt et OOOO O Figure 2 13 Forced oscillation omega 8 rad s Universal Mechanism 5 0 82 Getting Started Resonance In conclusion we consider the resonance case when the excitation frequency 1s equal to the natural frequency of the system 1 In the Pause window click the Interrupt button 2 In the Object simulation inspector set omega 5
45. ogram windows The List of windows tool Tools List of windows or A t 0 is used for switching between program windows object description windows in UM Input program and in UM Simulation program Es List of windows Fig 1 8 Switching between windows of object description in UM Input program Universal Mechanism 5 0 38 Getting Started Copy Paste of object elements 1 Activate ThreeLinkPend_Subs object see Fig 1 8 page 37 2 Come to Images element of tree of elements and select Support element 3 Copy the Support to clipboard Edit Copy to clipboard main menu com mand UM Object data input ThreeLinkPend File Edit Object Add Tools Help 4 Fe Copy to clipboard 4 ff To dipboard as component m lel Copy to file T Save as companen fe Insert E Ge Read From file EK Undo r mages El Support Fig 1 9 Copy to clipboard 4 Activate NineLinkPend object see Fig 1 8 page 37 5 Paste Support image element from clipboard Edit Paste New element will appear in list of Images 6 Select Object in element list and select Support in the Scene Image drop down list Universal Mechanism 5 0 39 Getting Started 1 5 2 1 2 Subsystems adding 1 Activate NineLinkPend object see Fig 1 8 page 37 2 Come to branch Subsystems in the model element tree add the new element and rename it to TLP_1 ThreeLinkPendulum_1 3 Select Subsystem type Included
46. on v New variable r y T LP_1 Pendulum1 appears in the container of variables 9 Add the same variable for each of the rest bodies of the multibody pendulum The Wizard of variables will be look like in the figure below Efe Wizard of variables ninelink pend User Expression All forces Jont force Coordinates Angular var Reaction F Linear var Bod By Pendulum TLP 1 Pendulumt i i i en Pendulum Typ Resolved in SC of body ee TLP 2 fj fra sco Pendulurat iy f w12 a B Pendulume C a C all r x ey C2 wy y Bese Fenduluma TLP_3 Fendulum Pendulume T Pendulurrs r y TLP_3 Pendulum3 4 Coordinates of point 0 0 0 of body TLP_3 Pe ad Y ry TLP_1 Fe ry TLP_3 Fe cy TLFP_1 Fe ry TLP_3 Fe cy TLF_1 Fe ry TLP_3 Fe yT LP 2 Pe yT LF_2 Pe yT LP_2 Pe Universal Mechanism 5 0 45 Getting Started Using the list of variables Let us save the created variables for the further usage with the help of List of variable tool 10 Create new list of variables Tools List of variables 11 Select all the variables from the container of the Wizard of variables and drag them to the List of variables window E List of variables 0 eH A Mo name cyTLPo1 Pendulumt Coordinates of point 0 0 0 of body TLP1 Pendulumd relative to Basel SC Basel projection r ce TLP_1 Perndulune Coordinates of point 0 0 0 of body TLP1 Pendulum relativ
47. onal degrees of freedorn Hl o OOOOOOOO0000 pA M Yr o OOOOOOOO0000 A jw z o 00000000000 A Rotational degrees of freedom Orientation angles A C M 2 hooomo SI C 3 hooomo 4 6 Set Weight to 1000 If a large weight e g 1000 is assigned to a joint in a closed loop it will be cut 7 Save model as ThreeLinkPend_Subs File Save as The improvement of the three body pendulum model is completed Now it can be used as a scheme Fig 1 7 A page 33 subsystem of nine body pendulum compound model according to A Universal Mechanism 5 0 37 Getting Started 1 5 2 1 Compound model creation Creating a new model 1 Close the UM Simulation program and come back to the UM Input program 2 Don t close ThreeLinkPend_Subs object Create new object New object of the File menu and save as NineLinkPend Then we will switch over with these two objects ThreeLinkPend_Subs and NineLinkPend necessarily 1 5 2 1 1 Scene image creation Let s prepare a scene image for the nine level pendulum model We will copy Support image from ThreeLinkPend_Subs model to NineLinkPend model As soon as the both objects are now open in UM Input program we will use Copy to clipboard Paste from clipboard tools One can also use Copy to file Paste from file tools to fulfill the coping action These tools are available for cop ing of any element of a model in UM Input program Choice of active object Switching between pr
48. projection r mel TLP_3 Pendulum Coordinates of point 0 0 0 of body TLRS Pendulum relative to Basel SC Basel projection r my TLP 3S Pendulum Coordinates of pom 0 0 0 of body TLP 3 Pendulum relative to Basel SC Basel projection r mel TLP_3 Pendulum Coordinates of point 0 0 0 of body TLRS Pendulum relative to Basel SC Basel projection r Lay off as absciss Time t 34 Drag the two last variables from the ninelinkpend tgr list of variables win dow to the graphical window Static plots of the variables will appear in the window 35 Start simulation 36 Point to the graphical window and make right mouse click on its Variable list panel Use the Read from text file item of the popup menu to load data from the results txt file Universal Mechanism 5 0 54 Getting Started Three pairs of plots corresponded to displacements of centers of mass of the two last pendulums are displayed in the graphical window now One can see that evaluated results first pair of plots and saved data second and third pairs of plots completely coincide The plot of the variables selected in the list of graphical window is marked with the line of double width Use this feature to make sure that the all three pairs of plots from the list are equal Pile Es Plots Variables ag coL 3 Pen tp TLP_Z Pen B TLF _3 Pen P Column 1 EE Column 2 2 37 3 95 Ex 1 Ey 1 A Universal Mechan
49. r As a result you have got a dy namic linked library UmTask dll containing equations of motion of your object The DLL is always located in the object directory When DLL of the object exists a model is ready for simulation Now we should generate and compile equations of motion and start UM Simulation for dynamical analysis of the system Paths to external compilers Universal Mechanism supports using Borland Delphi Borland C Builder Microsoft Visual C as external compilers 1 Select Tools Options menu item Your further actions depend on what external compiler you are going to use Delphi 2 Select Paths Delphi tab 3 Click Search Delphi button Borland C Builder Microsoft Visual C 2 Select Paths C tab 3 Click one of the following buttons Search Visual C or Search Borland C Builder depending on which C compiler is installed on your PC If UM successfully detects external compiler all paths are set automatically If the compiler is not found automatically e g if its newest version is not in cluded in the internal UM list of compilers paths to compiler and libraries should be set manually Universal Mechanism 5 0 21 Getting Started Generating and compiling equations of motion 1 Select Object Generate equations If your description of the model is correct the corresponding dialog box ap pears If your model description is not correct then tab Summary which contains all detected errors appe
50. ry Description Joint force Joint point axis Z 0 01 axis 0 0 1 Universal Mechanism 5 0 66 Getting Started 2 3 5 Creating force elements Now we will describe elastic and damping force elements between the top and the brick Let us use c parameter for the stiffness coefficient of the spring and mu parameters for the damping coefficient of the damper Length of the unloaded spring let us denote as 10 Select the jBrick joint Select the Joint force tab In the Joint force list select the Linear In the c box input c stiffness coefficient in the x0 box input 10 and set d to mu see Fig 2 4 Press Enter Set values of parameters as follows c 250 10 0 4 mu 5 RYN gt a Namek ataa Body Body Type Z Translational Geometry Description Joint force l 4 Joint force L Linear hi F FO c x xO d Q sin w t al FO c 0 d o a Figure 2 4 Elastic and damping joint forces Universal Mechanism 5 0 67 Getting Started 2 3 6 Visualization of spring and damper After all we have completely described object from the mechanical point of view We described all elements we need rigid bodies joints and force elements However our model now looks not so good spring and damper introduced as joint forces that cannot be visualized see the Fig 2 5 left In order to visualize spring and damper we will create two bipolar forces in the model Their values we
51. s for damped and free oscilla tions Using zero damping coefficient gives us free oscillations 1 Select the graphical window Point to the r z Brick variable in the list of va riables Open context menu Select the Copy as static variable menu com mand The second variable appears 2 Select the Pause inspector and click the Interrupt button Object simulation inspector appears Note The r z Brick variable which we dragged from the Wizard of va riables will be recalculated for every numerical experiment It is so called dynamic variable In order to compare plots for different expe riments we need to copy dynamic variables as static ones Static va riables are not changed from one experiment to another 3 Select the Object simulation inspector and point to the Identifiers tab 4 Set mu 0 and press Enter So we have just turned off damping Universal Mechanism 5 0 76 Getting Started 5 Click the Integration button It will take you some seconds to finish the simulation In the Fig 2 10 you can see the graphical window after two numerical experiments i Plots Pile Es il rz Brick Co Ex 1 Ey 1 F Figure 2 10 Graphical windows after the first experiment Universal Mechanism 5 0 77 Getting Started Free oscillation critical damping As we showed above critical damping coefficient is mu 100 Ns m Let us analyze the motion of the Brick in such a case 1 Point to the graphical windo
52. see Figure 3 Add new graphical object Figure 3 Adding a new element Note You can add new element of any type in the same way Universal Mechanism 5 0 9 Getting Started Renaming the graphical object As you create objects UM automatically assigns names to them Each name consists of a string containing the element type and a unique integer ID for that type UM named the recently created graphical element GO1 1 Point to the box with the name of the element and replace GOI with Sup port see Figure 4 z aes En Ges Sum ERRA Picar Sr ext attribute r Name of graphical G Peete graphical object Description GO positon object Type ak Te a Copy graphical object Add graphical element Figure 4 Renaming the graphical object Universal Mechanism 5 0 10 Getting Started Creating graphical elements Every graphical object GO can include any number of various graphical ele ments GE So you are able to create quite complicated images Let s create three elements sphere cone and box which form the image of the support altogether Creating new graphical element sphere 1 Click Add new graphical element button see Figure 4 New tab GEI appears see Figure 5 Support Support Type of graphical element Figure 5 Type of the graphical element 2 Choose type for the new graphical element Ellipsoid 3 Point to the Parameters tab and set a b c 0 05 4 Po
53. t Type B Rotational Universal Mechanism 5 0 52 Getting Started Comparison of results Let us compare the simulation results with the previously saved data and make sure that the different variants of description of joints between subsystems fig 1 7 scheme A and scheme B give identical results We will plot the Y displacement of the last two pendulums and compare them with the data from the file of calculated variables ninelinkpend tgr and the plots saved in the text file results txt 27 Select Object Simulation menu item UM Simulation program starts and loads the current model If autosave of configuration option is enabled pre viously created animation and graphical windows will be opened One can use Autosave tab of the Options window main menu Tools Options to enable autosave options 28 From the Analysis menu select Simulation Object simulation inspector ap pears 29 Point to the Initial conditions Coordinates tab If autosave of initial condi tions option is enabled previously values will be used Set 0 1 value for all the uncut joints as it is shown in the figure below if not Object simulation inspector Solver Initial conditions Object variables KVA Information Tools Coordinates Constraints for initials lt 0 0 L amp ninelnk pend Y r pper ekot pommer 0 1 U Support 1a OU 09983347 0 TLP_1 Pendulum 1 cut 99500416 0 TLP_1 Pendulum 2c eut 0 1 T TLFP_1 Pe
54. tive to Basel SC Basel Vector Universal Mechanism 5 0 30 Getting Started 1 5 Multibody pendulum We can use two approaches to develop multi link pendulum pendulum chain from the simple pendulum model First variant is the development of the simple pendulum model with copying of the existed elements Second variant is based on the usage of subsystem technique 1 5 1 Development of the simple pendulum model 1 Close the UM Simulation program and come back to the UM Input pro gram 2 Select Bodies and copy the pendulum two times Mame Comments T ext at A UA Delete body Add new body Oriented points Vectors Parameters Position Points Copy body Go to element ea Image W Visible Pendulum 3 Rename body Pendulum to Pendulum and new bodies to Pendulum2 and Pendulum3 4 Select Joints and copy jPendulum joint two times too Change the connecting bodies Penduluml and Pendulum2 for the second joint Pendulum2 and Pendulum3 for the third one Note Use the amp button in the top of the animation window to switch the mode of window Full object Single element 6 Save the model as ThreeLinkPend main menu item File Save as 7 Generate equations of motion with numerical iterative method Sect 1 3 7 1 page 19 8 Run UM Simulation 9 Create a new animation window 10 Select the Analysis Simulation menu item Universal Mechanism 5 0 31 Getting Started 11
55. ual directory or download using the following link http www umlab ru download 50 eng 07_um_simulation_examples pdf
56. ub systems with joints belong to the main compound object Fig 1 7 A Then we will make it by the means of body External and connection points Fig 1 7 B Compound object TLP subsystem Three Link Pendulum model Base Basic body Base0 Basic body O Joints O Joints gt Connections O Connection points Scheme A Scheme B Fig 1 7 Structure of the compound model of nine link pendulum Universal Mechanism 5 0 34 Getting Started 1 5 2 2 Subsystem preparation We should modify the existed model of three link pendulum ThreeLinkPend object to use it as subsystem of compound model Modification of kinematics As soon as we will describe rotational joint of the nine link pendulum suspen sion as an element of the compound model and rotational joints linking subsys tems will be an elements of compound model fig 1 7 scheme A or will be described in subsystems as joints with External body fig 1 7 scheme B joint jPendulum is not necessary in subsystem model Connectivity condition is necessary for any model of mechanical system It means that there must be a chain for each body that connects it with body O BaseO SCO Subsystem kinematics should be matched with kinematics of compound ob ject As soon as bodies of multi link pendulum are in planar motion three link pendulum model used as subsystem should enable motion of bodies in oscillation plane To enable mentioned conditions we will replace rotat
57. ubsystems External and included subsystems There are two variants of user created subsystems supported by Universal Me chanism software External subsystem creates the link to the existed model In cluded subsystems unlike the external ones belong to the compound object The object owns their structures bodies joints forces etc and parameters The most effective way to create nine pendulum model is the usage of the three link pendulum model as an external subsystem as soon as all subsystems are ki nematically identical On the other hand usage of included subsystems for com pound models creation is more common Hereupon we will use included subsystems in our example Description of interaction between subsystems Two methods can be used to connect bodies of different subsystems with joints or force elements 1 create necessary element joint or force element in the main compound ob ject 2 use special body called External for the description of elements in subsys tems In the second method it is necessary to point bodies and characteristic points called connection points of these bodies for joints and force elements which use external bodies Setting a connection means to point which body is ex ternal for considered element and which point of this body is characteristic for the element Universal Mechanism 5 0 dd Getting Started At the first stage of creation of nine link pendulum model we will connect s
58. user Object simulation inspector Solver Initial conditions Object variables VA Information Tools Coordinates Constraints for initials dgb D 0 L amp oe ninelnk pend Y Coordinate Velocity Comment Message 0 1 0 0 1 0 0 1 0 0 09983341 0 0 9950041 0 0 1 0 0 1 0 0 1 0 0 983441 29 0 3 001 46822 0 0 4 0 0 1 0 0 1 0 2 6r172699 0 5 31 922095 0 0 7 0 Number of dof 9 Mtegration Support 1a jTLP_12 14 ITLF_23 14 TLP_1 jPendulurn 1 c cut TLP_1 jPendulurn 2c cut TLP_1 jPendulurn 3alcut TLP_1 jPendulunme 14 TLP_1 jPendulurnas 1a TLP_ 2 jPendulurn 1 c cut TLP_2 Pendulum 2c cut TLP_2 Pendulurn 3alcut TLP_2 jPenduluriz 1a TLP_2 Pendulurns 14 TLP_3 jPendulurn 1 c cut TLP_ 3 Pendulum 2c cut TLP_3 Pendulurn 3alcut TLP_3 Pendulurni 1a TLP_3 jPendulurns 14 Getting Started Universal Mechanism 5 0 44 Getting Started Variables creation Let us use Wizard of variables to create a number of variables Y coordinate of the center of mass of each of the pendulums 4 Open the Wizard of variables Tools Wizard of variables 5 Point to the Linear var tab linear variables coordinates velocities accelera tions etc 6 Point to the tree of the object elements and select the Pendulum1 body of the TLP_1 subsystem 7 Select Y in the Component group of the Linear var tab 8 Then create the new variable to the container with the help of the butt
59. variable to the container clicking the v button Drag new variable to the animation window A list of animated vectors is hidden by default You can make it visible and change its position with the help of the Position of list of vectors command of the pop up menu of the animation window 6 Select animation window click right mouse button and select Position of the list of vectors Left To draw a trajectory of the pendulum create a new variable with the help of the master 7 Repeat all steps we made for the velocity but the Type of the variable set to r radius vector Drag this variable to the animation window 8 Double click on the velocity item in the List of vectors and select red col or for the vector of velocity and than double click trajectory item and se lect blue color for it 9 Click the Integration button in the Object simulation inspector Now you can see the vector of the velocity and trajectory of the center of the mass of the pendulum You should use the Scale of vectors command of a pop up menu to specify its scale Double click on an element of the list of vectors or on a vector trajectory image to change the color of the vector and trajectory in addition for the trajectory to change the number of points on the curve Universal Mechanism 5 0 29 Getting Started B Ko e7 ulh S amp Sle 2 Vectors Trajectories Ea v Fendulum Velocity of point 0 0 0 of body Pendulum rela
60. ws Select the first variable r z Brick and copy it a static one again use the Copy as static variable item from the context menu 2 Select the Pause inspector and click the Interrupt button Object simulation inspector appears 3 Select the Identifiers tab and set mu 100 4 Click Integration Now you can see that the motion of the brick 1s non periodic see the Fig 2 11 NIMIM Biel E it i 4 92 0 09239999 Ex 1 Ey 1 EA Varnables 1 rz Brick Co E r2 Brick Co Figure 2 11 Graphical window after three numerical experiments 5 Make numerical experiments for other values of the damping coefficient Do not forget to copy variables as static ones 6 If you changed the value of the damping coefficient set it again to mu 100 Ns m Universal Mechanism 5 0 78 Getting Started 2 4 2 Statistical analysis Now we will come through some additional tools for analysis of results of the simulation 1 From the Tools menu select Statistics New Statistics window appears 2 Drag the variable which corresponds to free oscillations from the graphical window to the Statistics window 3 Select the Statistics window and point to Power spectral density The characteristic shape of the power spectral density shows the process has the only frequency which corresponds to natural frequency We have the accurate ana lytical solution 5 rad s Not let us obtain this frequency numeri
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