Determination of Normal Acceleration in Planar Mechanisms by Means of Instantaneous Centres of Rotation

Abstract

The paper presents a new method for determination of normal accelerations which is based on the geometry of mechanisms. Every closed four-member kinematic group in planar mechanisms has the following characteristic: the vector of sum of relative normal accelerations between the kinematic pairs along the contour of the group is collinear with the line defined by relative instantaneous centres of rotation of the group members that are not in direct contact. This key characteristic of planar mechanisms allows the possibility of simple vector determination of unknown “normal“ components of acceleration in a mechanism on the basis of the known, given or unit normal acceleration of the driving member. When two members of a closed kinematic group constitute a sliding pair, constant relationship between the intensity of the Coriolis (and relative normal) acceleration of the kinematic pair with the relative normal acceleration of that member of the sliding pair whose constant centre of rotation lies on the contour can be established. The relationship is defined by absolute and relative instantaneous centres of the sliding pair. Determination of acceleration does not require that characteristic velocities of the mechanism members should be known.