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Advances in Robot Manipulators Part 10

Tham khảo tài liệu 'advances in robot manipulators part 10', kỹ thuật - công nghệ, cơ khí - chế tạo máy phục vụ nhu cầu học tập, nghiên cứu và làm việc hiệu quả | 352 Advances in Robot Manipulators Fig. 10. Evolution of the Z-configuration under external loading a b c Fig. 11. Model A Force-deflection relations and deformations in actuated joints for Z-configuration initial unloaded posture with coordinates 0 -30 02 30 Therefore the stiffness analysis of model A Table 2 allowed detecting more general class of manipulator postures that are dangerous with respect to the buckling. They include all configurations that posses an axial symmetry with respect to the direction of the external force S- and Z-configurations for instance . These postures will be in the focus of the stiffness analysis for models B and C. Configuration Critical force Stiffness for unloaded mode Stiffness near the buckling Ô 0 Stiffness for large deformations ô L F Fcr F Fcr S-configuration 00 O02 0 Kl L OT OT 0.20 Ặ L2 0.22 Ặ L2 n-configuration 00 02 -30 - 1.78 0 L2 - - 0.43 K Z-configuration 00 -30 02 30 1.03 L 16.7 K 5.50 K 0.20 Ặ L2 0.39 Ặ L2 Table 2. Summary of the Stiffness analysis for model A 5.3 Stiffness analysis for model B In this case it is assumed that the manipulator stiffness is caused by elasticity of the links while the actuating joints are rigid enough. The elastic deflections bending and Enhanced stiffness modeling of serial manipulators with passive joints 353 compression are still restricted by the Cartesian xy-plane and each link includes only three virtual springs with joint variables 0 x 0 and 9 tz which describe respectively linear displacements in x- and y-directions and angular rotation around z-axis. Totally the stiffness model has 11 variables two for a passive joint and nine for the virtual springs of three links so it was studied numerically using the proposed technique. The stiffness parameters were evaluated assuming that the links are rectangular beams of the length L and the cross-section axb where a 0.02L and b 0.05L . For comparison purposes corresponding stiffness matrices were scaled with respect to the bending .