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Flexibility optimization of a hexapod machine tool. (English) Zbl 1330.70025

Summary: Lightweigth structures like Stuart platforms for manufacturing processes and space application require low flexibility in order to guarantee high motion accuracy. In this paper two methods of flexibility optimization are presented and applied to design variants of a hexapod machine tool. The first one is based on a multibody system simulation (MBS). Here, the hexapod is modeled as a rigid multibody system under consideration of joint elasticities. Actuator amplitudes in the links associated with desired end-effector trajectories are computed by inverse kinematics. Hence, dynamic forces and torques are not considered and, as there is no closed-loop control realized so far in the model and the built machine, the actual rotational and translational positions of the end-effector deviate from the desired pose due to machining loads. These deviations serve as objective functions during the optimization. Further, the obtained results are verified by considering the linearized elastostatic behavior. As a second method, a more general optimization approach based on the tangential stiffness matrix is introduced. Here, the flexibility behavior of the machine is optimized considering the whole workspace. The results are then compared with the results from the MBS-based optimizations which consider only the poses on a sample trajectory.

MSC:

70B15 Kinematics of mechanisms and robots
74K99 Thin bodies, structures
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