Recursive Method for the Computation of theSOn,SOn,1, andISOn, Representation Matrix Elements

1971 ◽  
Vol 12 (2) ◽  
pp. 197-206 ◽  
Author(s):  
Kurt Bernardo Wolf
Keyword(s):  
Recursive Method ◽  
Matrix Elements

scholarly journals A Recursive Method for Finding Revolute-Jointed Manipulator Singularities

1995 ◽  
Vol 117 (1) ◽  
pp. 55-63 ◽  
Author(s):  
J. W. Burdick
Keyword(s):  
Jacobian Matrix ◽  
Screw Theory ◽  
Industrial Robot ◽  
Recursive Algorithm ◽  
Explicit Construction ◽  
Recursive Method ◽  
Matrix Elements ◽  
Screw Axis ◽  
Computational Burden ◽  
Singular Configurations

A geometric application of screw theory is used to develop a recursive algorithm for computing all singular configurations of revolute-jointed manipulators with arbitrary link geometries and an arbitrary number of joints. The depth of the recursion is linear in the number of joints, n, while the computational burden is proportional to 2n−2. This method does not require explicit construction of the Jacobian matrix elements or a determinant operation. The method is also robust with respect to the bifurcations that occur for industrial robot geometries. Further, the screw axis of the singular motion is determined at no additional cost.

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