GA\SQP optimization for the dimensional synthesis of a delta mechanism based haptic device design

Abstract When designing a 3 DOF DELTA haptic device, a challenging problem is to optimize all the design variables to enable the DELTA mechanism to provide a desired cube workspace and perform well in haptic display. The designed haptic device should be able to exert required forces to a user in the whole workspace. Moreover, used as a haptic joystick to be installed in a dashboard, the outline envelope of the DELTA mechanism and driving motors are strictly restricted. The dimensional constraints on the designed device put forward much higher request on the dimension synthesis of DELTA mechanism to satisfy the requirements of output force and cube workspace simultaneously. The special constraints make the design of DELTA haptic joystick different from conventional DELTA robot design. In this paper, we solve the problem by using Genetic algorithms (GA) and sequential quadratic programming (SQP) and develop a DELTA haptic device. Through transforming the objectives and the constraints step by step, all proposed constraints are satisfied very well. For a haptic device, we explain the physical meaning of the condition number of the Jacobian matrix in force domain and use it as the criteria to evaluate the performance of a mechanism in haptic display. Experimental results and the prototype clearly demonstrate that the combination of SQP and GA (SQP uses the result of GA as the start point of all design variables) gives the optimal solution.

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