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Haptics and Virtual Reality

Haptics and Virtual Reality. Lecture 6: Haptic interface kinematics. M. Zareinejad. Grounded interfaces. Very similar to robots Need Kinematics.  . Determine endpoint position Calculate velocities Calculate force-torque relationships. – – –. Sometimes need Dynamics

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Haptics and Virtual Reality

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  1. Haptics and Virtual Reality Lecture 6: • Haptic interface kinematics M. Zareinejad

  2. Groundedinterfaces Verysimilartorobots NeedKinematics   Determineendpointposition Calculatevelocities Calculateforce-torquerelationships – – – SometimesneedDynamics Ifyouareweakonthesetopics,youmaywant tocheckoutIntroductiontorobotics: mechanicsandcontrolbyCraig(1989).  

  3. Kinematics • Thinkofa manipulator/ interfaceasaset ofbodies connectedbya chainofjoints • Revolutemost commonforhaptic interfaces

  4. Orientation of a Body

  5. Homogenous Transforms

  6. Homogenous Transforms • Translation • Rotation

  7. Kinematics MovingbetweenJointSpaceandCartesianSpace Forwardkinematics:basedonjointangles,calculate end-effectorposition  

  8. Jointvariables Becarefulhowyoudefinejointpositions  Relative Absolute

  9. Absoluteforwardkinematics x=L1cos(1)+L2cos(2) y=L1sin(1)+L2sin(2)

  10. Relativeforwardkinematics x=L1cos(1)+L2cos(1+ 2) y=L1sin(1)+L2sin(1+2)

  11. D-H Parameters

  12. D-H Parameters

  13. InverseKinematics Usingtheend-effectorposition,calculatethe jointangles Notusedofteninhaptics   Butusefulforcalibration – Therecanbe:  Nosolution(workspaceissue) 1solution Morethan1solution – – –

  14. Example Twopossiblesolutions Twoapproaches:   algebraicmethod geometricmethod – –

  15. Example

  16. Velocity Recallthattheforwardkinematicstellsusthe end-effectorpositionbasedonjointpositions Howdowecalculatevelocity? UseamatrixcalledtheJacobian   

  17. FormulatingtheJacobian Usethe chainrule:  Take partial derivatives: 

  18. AssembleinaMatrix

  19. Singularities Mostdeviceswillhavevaluesof forwhichtheJacobianissingular Thismeansthatthedevicehaslostoneor moredegreesoffreedominCartesianSpace Twokinds:    Workspaceboundary Workspaceinterior – –

  20. SingularityMath Ifthematrixisinvertible,thenitisnon-singular  CancheckinvertibilityofJbytakingthe  determinantofJ.Ifitisequalto0,thenitis singular Canusethismethodtocheckwhichvaluesof θ willcausesingularities

  21. CalculatingSingularities Simplifytext:sin(1+2)=s12  Forwhatvaluesof1and2doesthisequal zero? 

  22. Evenmoreuseful…. TheJacobiancanbeusedtorelatejoint torquestoend-effectorforces: Whyisthisimportantforhapticdisplays?  

  23. Howdoyougetthisequation? Principleofvirtualwork –Statesthatchangingthe coordinateframedoes notchangethetotalwork ofasystem 

  24. Dynamic

  25. Homework #1 SensAble’sPhantoms Quanser Pantograph

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