A Matrix Representation and Motion Space Exchange Metamorphic Operation
The paper presents a matrix representation of mechanical chains based on proposed joint-axis matrix, and a matrix operation of joints orientation change metamorphic processes. A four elements joint-axis matrix with joints types and orientations is developed first, and an augmented adjacency matrix of kinematic chains is formed by adding the elements of joint-axis matrix into the corresponding positions of general adjacency matrix of kinematic chains. Then the matrix operation of metamorphic process is performed through changing the orientation of metamorphic joint of augmented planar mechanism to transform the configuration of the mechanism from planar to spatial one.
S. J. Li and J. S. Dai, "A Matrix Representation and Motion Space Exchange Metamorphic Operation", Advanced Materials Research, Vols. 308-310, pp. 2058-2061, 2011