1 / 28

Manipulator Dynamics

Introduction to ROBOTICS. Manipulator Dynamics. Dr. Jizhong Xiao Department of Electrical Engineering City College of New York jxiao@ccny.cuny.edu. Manipulator Dynamics. Mathematical equations describing the dynamic behavior of the manipulator For computer simulation

gavan
Télécharger la présentation

Manipulator Dynamics

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. Introduction to ROBOTICS Manipulator Dynamics Dr. Jizhong Xiao Department of Electrical Engineering City College of New York jxiao@ccny.cuny.edu

  2. Manipulator Dynamics • Mathematical equations describing the dynamic behavior of the manipulator • For computer simulation • Design of suitable controller • Evaluation of robot structure • Joint torques Robot motion, i.e. acceleration, velocity, position

  3. Manipulator Dynamics • Lagrange-Euler Formulation • Lagrange function is defined • K: Total kinetic energy of robot • P: Total potential energy of robot • : Joint variable of i-th joint • : first time derivative of • : Generalized force (torque) at i-th joint

  4. Manipulator Dynamics • Kinetic energy • Single particle: • Rigid body in 3-D space with linear velocity (V) , and angular velocity ( ) about the center of mass • I: Inertia Tensor: • Diagonal terms: moments of inertia • Off-diagonal terms: products of inertia

  5. Velocity of a link A point fixed in link i and expressed w.r.t. the i-th frame Same point w.r.t the base frame

  6. Velocity of a link Velocity of point expressed w.r.t. i-th frame is zero Velocity of point expressed w.r.t. base frame is:

  7. Velocity of a link • Rotary joints,

  8. Velocity of a link • Prismatic joint,

  9. Velocity of a link The effect of the motion of joint j on all the points on link i

  10. Kinetic energy of link i • Kinetic energy of a particle with differential mass dm in link i

  11. Kinetic energy of link i Center of mass Pseudo-inertia matrix of link i

  12. Manipulator Dynamics • Total kinetic energy of a robot arm Scalar quantity, function of and , : Pseudo-inertia matrix of link i, dependent on the mass distribution of link i and are expressed w.r.t. the i-th frame, Need to be computed once for evaluating the kinetic energy

  13. Manipulator Dynamics • Potential energy of link i : Center of mass w.r.t. base frame : Center of mass w.r.t. i-th frame : gravity row vector expressed in base frame • Potential energy of a robot arm Function of

  14. Manipulator Dynamics • Lagrangian function

  15. Manipulator Dynamics The effect of the motion of joint j on all the points on link i The interaction effects of the motion of joint j and joint k on all the points on link i

  16. Manipulator Dynamics • Dynamics Model

  17. Manipulator Dynamics • Dynamics Model of n-link Arm The Acceleration-related Inertia matrix term, Symmetric The Coriolis and Centrifugal terms Driving torque applied on each link The Gravity terms

  18. Example Example: One joint arm with point mass (m) concentrated at the end of the arm, link length is l , find the dynamic model of the robot using L-E method. Set up coordinate frame as in the figure

  19. Example

  20. Example Kinetic energy

  21. Example • Potential energy • Lagrange function • Equation of Motion

  22. Example: Puma 560 • Derive dynamic equations for the first 4 links of PUMA 560 robot

  23. Example: Puma 560 • Set up D-H Coordinate frame • Get robot link parameters • Get transformation matrices • Get D, H, C terms

  24. Example: Puma 560 • Get D, H, C terms

  25. Example: Puma 560 • Get D, H, C terms ……

  26. Example: Puma 560 • Get D, H, C terms

  27. Example: Puma 560 • Get D, H, C terms

  28. Thank you!

More Related