TAILIEUCHUNG - Parallel Manipulators New Developments Part 17

Tham khảo tài liệu 'parallel manipulators new developments part 17', kỹ thuật - công nghệ, cơ khí - chế tạo máy phục vụ nhu cầu học tập, nghiên cứu và làm việc hiệu quả | Design Analysis and Applications of a Class of New 3-DOF Translational Parallel Manipulators 471 I 6 a - b - dca 53 Deriving d from 53 and in view of 1 allows the generation of á a - b- l d max s_3 max ca if 2 a 90 if a 90 54 2 a - b l 3 which are the isotropy conditions resulting in an isotropic 3-PCR TPM. 7. Workspace determination As is well known with comparison to their serial counterparts parallel manipulators have relatively small workspace. Thus the workspace of a parallel manipulator is one of the most important aspects to reflect its working ability and it is necessary to analyze the shape and volume of the workspace for enhancing applications of parallel manipulators. The reachable workspace of a 3-PCR TPM presented here is defined as the space that can be reached by the reference point P. a Three-dimensional view. Fig. 5. Workspace of a 3-PCR TPM without constraints on C joints. b Top view a Three-dimensional view. Fig. 6. Workspace of a 3-PCR TPM with constraints on C joints. b Top view 472 Parallel Manipulators New Developments Analytical method The TPM workspace can be generated by considering 25 which denotes the workspace of the r-th limb i 1 2 3 . With the substitution of constant vectors 25 can be expanded into the following forms px d1ca - a - b 2 pz d1sa 2 12 55 2 56 pz d2 sa 2 1I 22 1 z x 1 r . IV3 z . x V3 I Px Py - ý d3Ca - a - b H Y Px Py dĩCa - a - b ĩ I I 57 pz d3sa 2 l2 As dt varying within the range of -dmax 2 dt dmax 2 each one of the above equations denotes a set of cylinders with the radii of l. The manipulator workspace can be derived geometrically by the intersection of the three limbs workspace. As a case study for a 3-PCR TPM with kinematic parameters described in Table 1 the workspace without the constraints on the stroke of passive C joints is illustrated in Fig. 5. With the consideration of the stroke limits of C joints the whole reachable workspace of the CPM is depicted in Fig. 6. It can be seen that the C joints .

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