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Advances in Robot Manipulators Part 13

Tham khảo tài liệu 'advances in robot manipulators part 13', kỹ thuật - công nghệ, cơ khí - chế tạo máy phục vụ nhu cầu học tập, nghiên cứu và làm việc hiệu quả | 472 Advances in Robot Manipulators Although the actuating forces can be decreased by varying the orientations of the moving platform the required maximum leg lengths increase as indicated in Figs. 8 a b . It means that a larger task space is necessary to accommodate the planned singularity-free path. 2 Time optimum For this problem the travel time tf is to be determined. Based on the singularity-free path planning algorithm the planned trajectory is shown in Fig.9 i.e. the line for ụ 1 with the corresponding minimal travel time tf 5.85 sec. Fig. 7. Actuating forces along planned paths with a constant orientation and b varied orientations 3 Energy efficiency Fig. 9 also shows the minimal-energy trajectory with the corresponding travel time tf 20.01 sec i.e. the line for ụ 0 . Compared with the time optimal trajectory planning reduction in the travel time is at the expense of a greater consumed energy a poorer fitness value and a larger force. 4 Mixed cost function On the Optimal Singularity-Free Trajectory Planning of Parallel Robot Manipulators 473 The cost function is defined as G ụX Ãt 1- f f Tl dt 36 The optimal singular free trajectories for ụ 0.3 0.6 and 0.8 with the corresponding determined travel time tf 7.758 6.083 and 6.075 sec are also respectively shown in Fig. 9. Time s b Fig. 8. Leg lengths along planned paths with a constant orientation and b varied orientations 5. Conclusions In this chapter a numerical technique is presented to determine the singularity-free trajectories of a parallel robot manipulator. The required closed-form dynamic equations for the parallel manipulator with a completely general architecture and inertia distribution .