# OSU ECE 5463 - Inverse-Manipulator-Kinematics-1 (7 pages)

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## Inverse-Manipulator-Kinematics-1

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- Pages:
- 7
- School:
- Ohio State University
- Course:
- Ece 5463 - Introduction to Real Time Robotics Systems

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Inverse Manipulator Kinematics 1 Read Chapter 4 and Appendix C I Introduction Forward kinematics Given joint angles compute the position of the gripper foot with respect to the base the body Inverse kinematics An opposite problem to the forward kinematics given the position of the gripper foot calculate the joint angles much harder Given Fixed Function of i di i 1 n qi II Use OSU Hexapod as an example n 3 6 Specify the position of the foot with 3 DOF Focus on the position only 1 0 0 0 1 Position of the foot in the foot coordinate frame is the position of the foot in the body coordinate frame Steps for solving the I K problem 1 Step a Isolate the manipulator leg transformation matrix 0 0 0 1 1 1 0 0 0 0 1 0 0 0 0 1 0 1 1 3 24 16 69 1 44 1 1 1 0 0 1 0 2 5 2 5 12 8 12 8 12 8 1 3 24 16 69 1 44 1 Steps for solving the I K problem 1 Step b Solve for qi i 1 2 3 How many equations in Step a 3 How to solve the equations Some special techniques have to be used Inverse Kinematics Procedure For simple manipulators i 0 90 di 0 Algebraic approach which gives a closed form solution not an iterative numeric approach Good example in the text Section 4 7 pp 117 121 which uses PUMA 560 robot Principle 1 Separate out the dependence on the joint angles between the right and left sides of the equation Principle 2 If two equations involved 2 joint angles which are about consecutive parallel axes then square and add the equations to solve for the angles Principle 1 details Separate out the dependence on the joint angles between the right and left sides of the equation 3 24 16 69 1 44 1 1 0 0 0 0 0 0 1 0 0 0 0 1 0 1 0 0 0 0 12 8 2 5 1 0 0 12 8 1 0 From the above you can solve for 1 1 44 3 24 16 69 1 44 1 Other two equations 2 5 3 24 3 24 16 69 16 69 12 8 Use Principle 2 to solve for 2 and 3 12 8

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