A generalized parameterization of T1 motion and its application to the synthesis of planar mechanisms

Prior development of T1 motion theory has used a second-order parameterization which maximally simplifies the theory and allows for a description of the kinematic geometry. In the T1 motion theory presented here, this parameterization is generalized and not limited to the second-order. The results of this generalized parameterization are more algebraically complex; however, a purely algebraic application of the theory to the motion synthesis problem is made possible without an a-priori recognition of the kinematic geometry. Examples of the synthesis of a four-bar mechanism for rigid-body guidance and a four-bar mechanism for function generation are presented.