Parallel Manipulators New Developments Part 5

Tham khảo tài liệu 'parallel manipulators new developments part 5', kỹ thuật - công nghệ, cơ khí - chế tạo máy phục vụ nhu cầu học tập, nghiên cứu và làm việc hiệu quả | Wire Robots Part I Kinematics Analysis and Design 111 1T linear motion of a point 2T planar motion of a point 1R2T planar motion of a body 3T spatial motion of a point 2R3T spatial motion of a beam 3R3T spatial motion of a body Fig. 2 a class 1T Fig. 2 b class 2T Fig. 2 c class 1R2T Fig. 2 e class 2R3T Fig. 2 d class 3T Fig. 2 f class 3R3T Here T stands for translational and R for rotational . It is notable that this definition is complete and covers all wire robots. The classification of Fang 2005 is similar to Verhoeven s approach. Here three classes are defined as IKRM Incompletely Kinematic Restrained Manipulators where m n CKRM Completely Kinematic Restrained Manipulators where m n RAMP Redundantly Actuated Manipulators where m n 1 This chapter as well as the next one focuses on CRPM and RRPM robots. For IRPM see . Maier 2004 . Inverse kinematics Inverse kinematics refers to the problem of calculating the joint variables for a given endeffector pose. For the class of robots under consideration those are the lengths of the wires comparable to the strokes of linear actuators. Therefore the kinematical description of a wire robot resembles the kinematic structure of a Stewart-Gough platform presuming the wires are always tensed and can thus be treated as line segments representing bilateral constraints. Modeling a wire robot as a platform which is connected to m points on the base 112 Parallel Manipulators New Developments by m bilateral constraints it is reasonable to denote the platform pose x B r T Ọ v and the base points Bbi i 1 i m referenced in the inertial frame . Besides that the platform connection points pi are referenced in the platform-fixed coordinate frame I - . .The orientation of the platform in the base frame is represented by the rotation matrix BRP . Note that throughout this chapter roll-pitch-yaw angles are used. Assuming the wires are led by point-shaped guidances . small ceramic eyes from the winches to the platform the base

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