# OSU ECE 5463 - Inverse-Manipulator-Kinematics-2 (9 pages)

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## Inverse-Manipulator-Kinematics-2

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- Pages:
- 9
- School:
- Ohio State University
- Course:
- Ece 5463 - Introduction to Real Time Robotics Systems

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Inverse Manipulator Kinematics 2 Read Chapter 4 and Appendix C Principle 2 details If two equations involved 2 joint angles which are about consecutive parallel axes then square and add the equations to solve for the angles Recall that using Principle 1 you obtain the following two equation 2 5 3 24 16 69 12 8 1 Constant let it be 3 24 16 69 12 8 2 Square 1 and 2 and add the two together 3 24 16 69 12 8 2 3 24 12 8 17 12 8 Using 3 one can solve for 3 How to solve for 2 2 16 69 12 8 82 94 427 26 3 Approach for 2 Separate 2 move it to the left 3 24 16 69 1 44 1 1 0 0 0 0 1 0 0 0 2 5 2 5 0 1 1 0 0 0 0 0 0 1 0 12 8 0 0 1 3 24 16 69 1 44 1 From the first two equations you can obtain the following 2 5 3 24 2 5 3 24 16 69 12 8 16 69 Approach for 2 continued From the above two equations you can obtain the following Now you have three sets of equations For 1 1 44 For 3 82 94 For 2 see the top 427 26 Solve for review trigonometric functions 1 44 Convert to cylindrical coordinates where 0 1 44 Is the solution in the second or third quadrant it usually generates two solutions Solve for 82 94 427 26 Similar to 1 also two solutions 435 2 79 02 Solve for In general if we have two equations as the above we have only one solution So how many solutions we could have 2 1 2 4 Are those solutions physically possible OSU Hexapod Front View 3 Two solutions for 3 Knee up natural Knee down green not physically possible Two solutions for 1 Outside the body natural Inside the body not physically possible 3 1 1

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