A NEW VECTOR THEORY FOR THE ANALYSIS OF SPATIAL MECHANISMS

This paper develops a vector theory for the analysis of spatial mechanisms on the basis of the vector analysis theory and dual-number algebra and the recursive notation presented by J. Duffy. The theory includes the displacement, velocity and acceleration equations for open kinematic chains and loop mechanisms. The displacement equations for the loop mechanisms are classified into four groups with two forms, namely the primary, secondary, projective and fourth group loop/half-angle equations which have been applied to the derivation of the 16th degree polynomial input-output equations in the tan-half angle of the output angular displacements for the general spatial 7-link 7R and 6R-P mechanisms. In the analysis of the velocity and acceleration, the differential calculus is changed into vectorial algebraic operations and the unified equations are expressed in the vector forms which are linear in the velocity and acceleration variables.