tailieunhanh - Advanced Strategies For Robot Manipulators Part 4

Tham khảo tài liệu 'advanced strategies for robot manipulators part 4', kỹ thuật - công nghệ, cơ khí - chế tạo máy phục vụ nhu cầu học tập, nghiên cứu và làm việc hiệu quả | DeLiA A New Family of Redundant Robot Manipulators 81 Spherical Spherical these spherical joints require each one more of the usual three infinitesimal screws indicating concurrent revolute joints. Furthermore before do any further in order to solve the inverse velocity and acceleration analyses it is necessary the introduction of auxiliary screws with the purpose to satisfy an algebraic requirement with this consideration in mind the revolute joints are modeled as cylindrical joints in which the corresponding translational velocities are equal to zero. In other words 0 1 6 Ũ7 0 i 1 2 3 . Fig. 3. Infinitesimal screws of three representative limbs of the robot D1 Let AaC and A vO be respectively the angular and linear velocities of a point O attached at the end-effector-platform. The velocity state or twist about a screw of the end-effector-platform with respect to the fixed platform six- dimensional vector A VC Aac A vO r can be obtained trough the coupler and fixed platforms as A VC A VB B VC O O O 18 where AVB is the velocity state of the coupler platform with respect to the fixed platform and BVC is the velocity state of the end-effector-platform with respect to the coupler platform. Furthermore these kinematic states can be written in screw form as V J Q .V e fA VBB VC ỉ i 123 i e f O O O A 19 82 Advanced Strategies for Robot Manipulators where the Jacobians J e A JB B Jc A Jc are given by AtC _ r12 13 13 14 14 15 15 16 16 17 17 181 Ji -I i i i i i J BtC _ r6 7 7 8 8 9 9 10 10 11 11 121 Ji L i i i i i i J AtB _ r0 1 1 2 2 3 3 4 4 5 5 61 Ji - i i i i i iJ whereas Q e AQ B B Q c A ft c are matrices containing the joint rate velocities. In fact Q i - 12 13 13 14 14 15 15 16 16 17 17 18J Q i - 6 7 7 8 8 9 9 10 10 11 11 12 J Q i - 0 1 1 2 2 3 3 4 4 5 5 6J 20 21 The inverse velocity analysis consists of finding the joint rate velocities of the robot given a prescribed velocity state of the end-effector-platform with respect to the fixed platform A Vc . This .