For under-constrained and redundant parallel manipulators, the actuator inputs are studied with bounded variations in parameters and data. Problem is formulated within the context of force analysis. Discrete and analytical methods for interval linear systems are presented, categorized, and implemented to identify the solution set, as well as the minimum 2-norm least-squares solution set. The notions of parameter dependency and solution subsets are considered. The hyperplanes that bound the solution in each orthant characterize the solution set of manipulators. While the parameterized form of the interval entries of the Jacobian matrix and wrench produce the minimum 2-norm least-squares solution for the under-constrained and over-constrained systems of real matrices and vectors within the interval Jacobian matrix and wrench vector, respectively. Example manipulators are used to present the application of methods for identifying the solution and minimum norm solution sets for actuator forces/torques.
On the Solutions of Interval Systems for Under-Constrained and Redundant Parallel Manipulators
Manuscript received April 12, 2017; final manuscript received August 23, 2017; published online September 26, 2017. Assoc. Editor: Raffaele Di Gregorio.
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Notash, L. (September 26, 2017). "On the Solutions of Interval Systems for Under-Constrained and Redundant Parallel Manipulators." ASME. J. Mechanisms Robotics. December 2017; 9(6): 061009. https://doi.org/10.1115/1.4037803
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