Parallel Manipulators New Developments Part 13

Tham khảo tài liệu 'parallel manipulators new developments part 13', kỹ thuật - công nghệ, cơ khí - chế tạo máy phục vụ nhu cầu học tập, nghiên cứu và làm việc hiệu quả | Principal Screws and Full-Scale Feasible Instantaneous Motions of Some 3-DOF Parallel Manipulators 351 S S0 S rX S l m n p q r where S is a unit vector along the straight line l m and n are three direction cosines of S p q and r are the three elements of the cross product of r and S r is a position vector of any point on the line or the line vector. S S0 is also called Plucker coordinates of the line vector and it consists of six components in total. For a line vector we have S S0 0 . When S S 1 it is a unit line vector. When S0 0 the line vector S 0 passes through the origin point. When S S0 0 it is defined as a screw S S0 S r X S hS 1 When S S 1 it is a unit screw. The pitch of the screw is h S S0 S S If the pitch of a screw is equal to zero the screw degenerates into a line vector. In other words a unit screw with zero-pitch h 0 is a line vector. The line vector can be used to express a revolute motion or a revolute pair in kinematics or a unit force along the line in statics. If the pitch of a screw goes to infinity h X the screw is expressed as 0 S 0 0 0 l m n and called a couple in screw theory. That means a unit screw with infinity-pitch h X is a couple. The couple can be used to express a translation motion or a prismatic pair in kinematics or a couple in statics. S is its direction cosine. Both the revolute pair and prismatic pair are the single-DOF kinematic pair. The multi-DOF kinematic pair such as cylindrical pair universal joint or spherical pair can be considered as the combination of some single-DOF kinematic pairs and represented by a group of screws. The twist motion of a robot end-effector can be described by a screw. The linear velocity Vp of a selected reference point P on the end-effector and the angular velocity M of the endeffector are given according to the task requirements. Therefore the screw of the endeffector can be expressed by the given kinematic parameters Vp and M i w e vo w e vP rP X w where e is a dual sign VV is the velocity of

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