tailieunhanh - Advances in Robot Manipulators Part 8

Tham khảo tài liệu 'advances in robot manipulators part 8', kỹ thuật - công nghệ, cơ khí - chế tạo máy phục vụ nhu cầu học tập, nghiên cứu và làm việc hiệu quả | 272 Advances in Robot Manipulators 1 0 0 Ì S 0 S 1 S 0 10 J 10 J 11J S T Si- U l S S x T S- Uj 0i S x T S- U i 1 2 5. Workspace Mechanical constraints There are four main mechanical constraints that limit the workspace of a parallel manipulator 1 i Workspace singularities ii the actuators stroke iii the range of the passive joints and iv the link interference. Workspace singularities Fig. 3. The relationship between the determinant of jacobian matrix and 01X 02 The theoretical workspace of the manipulator is surrounded by singular surface. In the theoretical workspace the determinant of jacobian matrix q should be always greater or less than zero. The relationship between the determinant of jacobian matrix and parameters of Ỡ1X Ỡ2 for r 150 R 200 a n 2 p n 6 and Ỉ0 300 is shown in Fig. 3. If we set Ỡ1 Ỡ2 0 as the initial oriention the determinant of jacobian matrix should be always greater than zero. q 0 9 Actuators stroke The limited stroke of actuator i imposes a length constraint on link i such that max in i min i 0 1 2 10 Dimensional Synthesis and Analysis of the 2-UPS-PU Parallel Manipulator 273 where Zimin and limax are respectively the minimum and maximum lengths of leg i. Range of the passive joints Each passive joint has a limited range of motion. Let the maximum misalignment angle of the Universal joint Ui be ỡiumax Then the limits on Universal joint Ui impose a constraint such that 6u 6umax 11 Similarly Let the maximum misalignment angle of the spherical joint Si be ỡismax Then the limits on spherical joint Si impose a constraint such that 6iS eismax 12 Link interference Let us assume that the links can be approximated by cylinders of diameter D. This imposes a constraint on the relative position of all pairs of links such that distance l Ij D i j 0 1 2 i jỉ 13 or the minimum distance between every two line segments corresponding to the links of the parallel manipulator should be greater than or equal to D. The minimum .