Title :
The eigenscrew decomposition of spatial stiffness matrices
Author :
Huang, Shuguang ; Schimmels, Joseph M.
Author_Institution :
Dept. of Mech. & Ind. Eng., Marquette Univ., Milwaukee, WI, USA
fDate :
4/1/2000 12:00:00 AM
Abstract :
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
Keywords :
eigenvalues and eigenfunctions; elasticity; flexible manipulators; manipulator kinematics; matrix algebra; coordinate transformation invariance; eigenscrew decomposition; elastic devices; kinematically unconstrained rigid body; manipulator system; matrix decomposition; rank-1 matrices; rank-1 stiffness matrices; rotational components; spatial stiffness matrices; stiffness matrix primitives; stiffness-coupling index; translational components; Eigenvalues and eigenfunctions; Frequency synthesizers; Impedance; Industrial engineering; Matrix decomposition; Orbital robotics; Robot kinematics; Robotic assembly; Robotics and automation; Springs;
Journal_Title :
Robotics and Automation, IEEE Transactions on