Notation and General Equations for the Kinematics of Planar Mechanisms

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Abstract
This paper describes a notation for the kinematic properties of an assembly of co-planar laminae. Such an assembly may include a lamina capable of deformation in certain ways. The notation enables the user to write down a set of equations, called symbolic equations, which determine the movability of the assembly, or its degree of redundancy should it be a structure; and a further set called kinematic equations, which determine relative displacements, velocities and accelerations. Examples are given to show the use of the notation for the description of various mechanisms and the determination of their movability. A solution of the kinematic equations for a 4-bar linkage is given, and its use in analysis and design described. The use of this notation in the synthesis of linkages is discussed, and the possibilities of the single closed chain enumerated completely.

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