Torque
*10E3 function evaluations Torque
*10E3 function evaluations Torque
*10E3 function evaluations Torque
*10E3 function evaluations
SGA 7。90 9777 5。94 9777 5。 50 3。71
GAE 5。38 4801
4862 3。34 2。 19
DE 3。10 1260
1200 2。77 1。68
The optimization results summarizing the torque and function evaluations for the SCARA manipulator for the various cross-sections are shown in Table VIII。 The rect- angular cross-section provides minimum torque for the defined task without violating any of the constraints。 The objective function history for the SCARA manipulator for each cross-section is shown in Fig。 7。 It is observed that the DE converges faster than the other two in about 20 generations and in a monotonic fashion。
OPTIMUM ROBOT DESIGN
FIGURE 7 SCARA manipulator objective function history。
4。2。 3-DOF Articulated
A 3-DOF articulated PUMA type manipulator along with the modeling DH param- eters are shown in Fig。 8。 The last two links were optimized but the objective function included the torque from all three joints。 The task specification and constraints are given in Table IX。 The constraint values for the design variables were the same for all three optimization approaches。
The results of the optimization process utilizing the three evolutionary techniques are presented in Tables X—XII。 In these tables, the values of the design variables for each cross-section and the torque and number of function evaluations for each technique are presented。 The length values obtained satisfy the kinematic requirements (the manipulator reaches the desired points without violating any constraints) and along with the link parameters (cross-section and Young's modulus) the structural require- ments。 It is observed that the DE approach consistently obtains smaller torques and smaller number of function evaluations。 The number of function evaluations is an indi- cation of the computing effort required in reaching the optimum torque。
The optimization results summarizing the torque and function evaluations for the articulated manipulator for the various cross-sections are shown in Table XIII。 The square cross-section provides for the minimum torque for the defined task while 机器人优化设计英文文献和中文翻译(8):http://www.youerw.com/fanyi/lunwen_82103.html