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Parallel Manipulators Towards New Applications Part 15

Tham khảo tài liệu 'parallel manipulators towards new applications part 15', kỹ thuật - công nghệ, cơ khí - chế tạo máy phục vụ nhu cầu học tập, nghiên cứu và làm việc hiệu quả | Mobility of Spatial Parallel Manipulators 483 The Plucker coordinates of the specified motions should be firstly expressed in a Cartesian coordinate system. This chapter supposes that the twists of the free motion s of the endeffector are denoted by End. Step 2 Solve the constraint s exerted to the end-effector by its kinematic chain s . According to reciprocities between free motion s and constraint s of an end-effector the constraint s applied to the end-effector can be solved with the equation 16 z .7 f. F Yr. c I SEnd I E End 29 0 where End indicates the specified free motion s of the end-effector and End denotes any constraint applied to the end-effector. Step 3 Decide the number of kinematic chains m m 1 that will be used to connect the end-effector with the fixed base. If every link in the chain is connected to at least two other links the chain forms one or more closed loops and is called a closed kinematic chain if not the chain is referred to as open Shigley Uicker 1980 . For the later open chain case the synthesis is simply stated as any kinematic chain is feasible if the twist basis g of the chain contains End . However the following steps should be further discussed if the mechanism is a closed one. Step 4 Synthesize the terminal constraint s of each kinematic chain. Suppose c SEnd - I SEnd End Cn 1 c SEnd I 30 where n indicates the dimension of the constraint basis of the end-effector. Suppose that the terminal constraint s of the r th i 1 2 m kinematic chain is denoted by Sj the terminal constraint s of the chain might be synthesized with _c .c - End Kị 31 where Kị k -i Kị2 - Kin and Ký- ịkfí kị2 - kinỴ and j U - nt . For a feasible mechanism that makes the end-effector only have the prescribed free motion s the necessary and sufficient criterion is that the resultant terminal constraint s of .1 1 . . 1 . m . 1 1 1 1 . 1 . . r-C .1 . all these m kinematic chain s c should be equivalent to End. This is called the construction criterion 1 of the .