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Geometric Design of 3R Robot Manipulators for Reaching Four End-Effector Spatial Poses

In this paper, the four-precision-point geometric design problem of serial-link robot manipulators with three revolute joints is solved using a polynomial continuation method. At each precision point, the end-effector spatial locations are defined. The dimensions of the geometric parameters of the 3R manipulator are computed so that the manipulator’s end-effector will be able to reach these four pre-specified locations. Denavit and Hartenberg parameters and 4 × 4 homogeneous matrices are used to formulate the problem and obtain the design equations. Three of the design parameters are set as free choices and their values are selected arbitrarily. Two different cases for selecting the free choices are considered and their design equations are solved using polynomial homotopy continuation. In both cases for free choice selection, 36 distinct manipulators are found, the end-effectors of which can reach the four specified spatial positions and orientations.