Design Optimization of a Parallel–Serial Manipulator Considering Stiffness Criteria

In this paper, we analyze stiffness and perform geometrical optimization of a parallel–serial manipulator with five degrees of freedom (5-DOF). The manipulator includes a 3-DOF redundantly actuated planar parallel mechanism, whose stiffness determines the stiffness of the whole mechanical system. First, we establish the kinematic and stiffness models of the mechanism and define its stiffness matrix. Two components of this matrix and the inverse of its condition number are chosen as stiffness indices. Next, we introduce an original two-step procedure for workspace analysis. In the first step, the chord method is used to find the workspace boundary. In the second step, the workspace is sampled inside the boundary by solving the point-in-polygon problem. After that, we derive stiffness maps and compute the average stiffness indices for various combinations of design variables. The number of these variables is reduced to two geometrical parameters, simplifying the representation and interpretation of the obtained results. Finally, we formulate the multi-objective design optimization problem, whose main goal is to maximize the lateral stiffness of the mechanism. We solve this problem using a hierarchical (ε-constraint) method. As a result, the lateral stiffness with optimized geometrical parameters increases by 54.1% compared with the initial design.