A study of the instantaneous centers of velocity for 1-dof and 2-dof planar linkages

Abstract

This paper presents a detailed study of the instantaneous centers of velocity (henceforth referred to as instant centers) and the lines containing the instant centers for one-degree-of-freedom (1-dof) and two-degree-of-freedom (2-dof) planar linkages with up to 11 links. The focus is on graphical methods to locate secondary instant centers (that is, instant centers which are unknown from inspection and require graphical construction) or the lines containing secondary instant centers. The secondary instant center for a pair of links with one relative degree of freedom is a unique point, and for a pair of links with two relative degrees of freedom the secondary instant center must lie on a unique line. For a 2-dof linkage, the problem of finding the unique locations of the secondary instant centers on these lines is not addressed in this paper (this would correspond to knowing the ratio of the two input velocities). The paper reviews known graphical methods for the 4-bar, 5-bar, 6-bar, and 7-bar linkages and then presents original graphical methods to locate the secondary instant centers for the 1-dof 8-bar and 10-bar linkages, and the lines containing the secondary instant centers for the 2-dof 9-bar and 11-bar linkages.