A configuration of a mechanical linkage is defined as regular if there exists a subset of actuators with their corresponding Jacobian columns spans the gripper's velocity space. All other configurations are defined in the literature as singular configurations. Consider mechanisms with grippers' velocity space . We focus our attention on the case where m Jacobian columns of such mechanism span , while all the rest are linearly dependent. These are obviously an undesirable configuration, although formally they are defined as regular. We define an optimal-regular configuration as such that any subset of m actuators spans an m-dimensional velocity space. Since this densely constraints the work space, a more relaxed definition is needed. We therefore introduce the notion of k-singularity of a redundant mechanism which means that rigidifying k actuators will result in an optimal-regularity. We introduce an efficient algorithm to detect a k-singularity, give some examples for cases where m = 2, 3, and demonstrate our algorithm efficiency.
Optimal-Regularity for Serial Redundant Robots
Manuscript received May 15, 2016; final manuscript received December 15, 2016; published online March 24, 2017. Assoc. Editor: Andreas Mueller.
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Shvalb, N., Grinshpoun, T., and Medina, O. (March 24, 2017). "Optimal-Regularity for Serial Redundant Robots." ASME. J. Mechanisms Robotics. June 2017; 9(3): 031015. https://doi.org/10.1115/1.4035532
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