Accessible Region and Synthesis of Robot Arms

The present paper deals with the study of determining accessible region for two and three-link robotic arms with pin-joints. Based on the derivation of the loci-curves traced by a two-link robotic arm, design charts are developed. Such design charts are utilized in determining the accessible regions of a three-link robotic arm. Following the analysis of the accessible regions of two and three-link robotic arms, the paper presents a synthesis procedure to synthesize two and three-link robotic arms. Given a set of end-positions of a two or three-link robot arm, the proposed synthesis procedure will yield the dimensions and the location of the robot arm which will enclose within its accessible region the design points. The same synthesis procedure is proposed to trace a specific planar point-path. The present paper further examines the potential application of the synthesis procedure of two and three-link robotic arms in synthesizing a closed-loop mechanism for point-path generation. The two-link robotic arm is examined for the case where the end positions lie on a fixed circle. This case leads to the synthesis of a four-bar mechanism for a special point-path curve. The synthesis procedure may be extended from the four-bar synthesis to a cam-follower (non-circular-cam) system where the follower is the two link robotic arm. A further extension of this procedure is demonstrated in synthesizing analytically the dual-cam mechanisms derived from the stephenson six-link mechanism. The present investigation examines all three possible cases of dual-cam mechanisms. For special cases, it is demonstrated that such dual-cam mechanism may be degenerated to synthesize a mechanism with one cam pair.