First-Order Coordination of the Articulated Arm Subassembly Using Curvature Theory

This paper presents an approach to obtain the first-order speed ratios for three-degree-of-freedom spatial mechanisms that allow three degrees of translational freedom. The approach eliminates the need to locate the canonical frame and find the instantaneous invariants of motion and provides a direct method of obtaining the first-order speed ratios. The expressions for the speed ratios of the articulated arm subassembly are analyzed, and the regions of the workspace wherein the joints have dwells in their trajectories are identified. The first-order Taylor series is used for joint coordination, allowing the system to track a predefined spatial path. An example illustrating the application of curvature theory to spatial path tracking with a specific articulated arm subassembly is presented.Copyright © 2007 by ASME