Kinematics for robotics inverse and forward
- 1. D R . T A R E K A . T U T U N J I M E C H A T R O N I C S E N G I N E E R I N G D E P A R T M E N T P H I L A D E L P H I A U N I V E R S I T Y , J O R D A N 2018 Robotics: Kinematics
- 2. Outline Description and Transformation Rigid Body Pose Rotation Matrix Euler Angles Homogeneous Transformation Direct Kinematics DH Convention Manipulator Kinematics Work Space Inverse Kinematics
- 5. Elementary Rotations Rotated by angle a about the z-axis
- 8. Example
- 12. Inverse Problem
- 13. Rotating Frame (Euler Angles): ZYZ https://www.youtube.com/watch?v=q0jgqeS_ACM
- 15. Kinematics Manipulator consists of a series of links connected by means of kinematic pairs of joints Base End-Effector Degrees of Freedom (DoF)
- 16. Revolt vs. Prismatic Joints
- 17. Direct Kinematics The objective of direct kinematics is to compute the position and orientation of the end-effector as a function of joint variables. https://www.youtube.com/watch?v=jTAtaPrN2CI
- 19. Example
- 20. Open vs. Closed Chain Open-chain manipulators have n+1 links connected by n joints. Each joint provides a single DOF Closed-chain manipulators contain at least one loop and therefore the number of joints l is equal or greater than number of links n.
- 21. KUKA KR-270
- 25. DH Classical vs. Modified
- 26. Kinematics of Typical Manipulator Structures 1. Three-Link Planar Arm 2. Parallelogram Arm 3. Spherical Arm 4. Anthropomorphic Arm 5. Spherical Wrist 6. Spherical Arm + Spherical wrist (Stanford Manipulator) 7. Anthropomorphic arm + Spherical Wrist 8. DLR Manipulator 9. Humanoid Manipulator
- 27. Example: Three-Link Planar Arm
- 28. Example: Three-Link Planar Arm
- 29. Example: Three-Link Planar Arm
- 34. Example: Anthropomorphic Arm with Spherical Wrist
- 35. Joint Space and Operational Space The direct kinematics equation of a manipulator allows the position and orientation of the end-effector frame to be expressed as a function of the joint variables w.r.t. the base frame. The position can be given by the coordinates with regard to the geometry structure while the orientation can be specified in terms of the Euler angles Position Orientation • It can also be written in a form of the joint space where Is the angle for revolt joint and distance for prismatic joint
- 36. Workspace Workspace is the reachable configurations of the end effector
- 37. Kinematic Calibration Kinematic calibration techniques are devoted to find accurate estimates of DH parameters from a series of measurements on the manipulator’s end effector pose.
- 38. Inverse Kinematics Objective is the determination of the joint variables corresponding to a given end- effector position and orientation. This is a much more complex problem when compared to direct kinematics
- 39. Inverse Kinematic Examples 1. Three-link Planar Arm 2. Manipulators with Spherical Wrists 3. Spherical Arm 4. Anthropomorphic Arm 5. Spherical Wrist
- 40. Example: Three-link Planer Arm
- 41. Example: Three-link Planer Arm
- 42. Example: Three-link Planer Arm And finally Gives
- 43. Example: Three-link Planer Arm
- 44. Reference Siciliano, Sciavicco, Villani, and Oriolo. Robotics: Modeling, Planning, and Control. Advanced Textbooks in Control and Signal Processing. Springer 2009