The Eigenscrew Decomposition of Spatial Stiffness Matrices

Document Type




Format of Original

11 p.; 28 cm

Publication Date



Institute of Electrical and Electronics Engineers (IEEE)

Source Publication

IEEE Transactions on Robotics and Automation

Source ISSN


Original Item ID

doi: 10.1109/70.843170


A manipulator system is modeled as a kinematically unconstrained rigid body suspended by elastic devices. The structure of spatial stiffness is investigated by evaluating the stiffness matrix “primitives”-the rank-1 matrices that compose a spatial stiffness matrix. Although the decomposition of a rank-2 or higher stiffness matrix into the sum of rank-1 matrices is not unique, one property of the set of matrices is conserved. This property, defined as the stiffness-coupling index, identifies how the translational and rotational components of the stiffness are related. Here, we investigate the stiffness-coupling index of the rank-1 matrices that compose a spatial stiffness matrix. We develop a matrix decomposition that yields a set of rank-1 stiffness matrices that identifies the bounds on the stiffness-coupling index for any decomposition. This decomposition, referred to as the eigenscrew decomposition, is shown to be invariant in coordinate transformation. With this decomposition, we provide some physical insight into the behavior associated with a general spatial stiffness matrix.


IEEE Transactions on Robotics and Automation, Vol. 16, No. 2 (April 2000): 146-156. DOI.