A Matrix Method of Displacement Analysis of the General Spatial 7R Mechanism

An input-output equation of the general spatial 7R mechanism is derived in this paper by using the method in [1] and applying the rotation matrices. The result is the same as [2], but the process of derivation is simpler. Applying the character of rotation matrices, it is not difficult to obtain the recurrence formulas of direction cosines of Cartesian unit vectors, to calculate the scalar products and triple products of these unit vectors, and to derive the 6th constraint equation. Moreover, an algorithm, which consists of successive applications of row transformation and expansion based on Laplace's Theorem, is given to evaluate the 16×16 determinant according to its characteristic, so that the evaluation is much simplified.