On Displacement Analysis of the RSSR-SS Mechanism

Abstract

Abstract This article presents a method for performing (RSSR-SS) mechanism displacement analysis. The benefit of this method is that it provides a practical alternative for performing RSSR-SS mechanism displacement analysis and is fully applicable with today's mathematics software. This method is an extension of the adjustable RSSR-SS synthesis method developed by the authors (Suh, C. H., Radcliffe, C. W. (1978 Suh, C. H. and Radcliffe, C. W. 1978. “Kinematic analysis of spatial mechanisms”. In Kinematics and Mechanism Design pp. 179–183. New York: John Wiley and Sons. [Google Scholar]). Kinematic analysis of spatial mechanisms. In: Kinematics and Mechanism Design. New York: John Wiley and Sons, pp. 179–183). By utilizing the passive degree of freedom of the coupler of the RSSR mechanism and its design equations (Sandor, G. N., Erdman, A. G. (1984 Sandor, G. N. and Erdman, A. G. 1984. “Spatial mechanisms with an introduction to robotics”. In Advanced Mechanism Design Analysis and Synthesis pp. 635–641. Englewood Cliffs: Prentice-Hall. [Google Scholar]). Spatial mechanisms with an introduction to robotics. In: Advanced Mechanism Design Analysis and Synthesis. Englewood Cliffs: Prentice-Hall, pp. 635–641), the design equation for the remaining (S-S) link of the RSSR-SS mechanism was developed using spatial transformation matrices under the constant length condition of the remaining S-S link. The angular rotation about the coupler of the RSSR mechanism, satisfying the constant length equation of this remaining S-S link, was calculated, numerically (Allen M. B. III, Isaacson, E. L. (1998 Allen, M. B. III and Isaacson, E. L. 1998. “Solution of non-linear equations”. In Numerical Analysis for Applied Science pp. 177–187. New York: John Wiley and Sons. [Google Scholar]). Solution of non-linear equations. In: Numerical Analysis for Applied Science. New York: John Wiley and Sons, pp. 177–187). As an example, the displacement of a series of rigid body points on the coupler of an adjustable RSSR-SS mechanism was calculated for a range of prescribed crank angles.