Dexterity measures and their use in quantitative dexterity comparisons

Abstract

The majority of proposed dexterity measures rely on the use of the condition number of the manipulator’s Jacobian matrix mapping actuator velocities to end effector velocities. Unfortunately, for the vast majority of manipulators, the conventional Jacobian matrix has inconsistent units making the aforementioned measures dependent on units and scale. Recently, a Jacobian matrix mapping the joint velocities to independent Cartesian velocity components of three points on the end effector was proposed. In most cases, this Jacobian matrix has consistent units and in many cases it is dimensionless. This dimensionally-homogeneous Jacobian matrix yields meaningful dexterity measures that allow quantitative dexterity comparisons between manipulators with different architectures. Although these new measures were originally proposed within the context of parallel manipulator design and analysis, they can also be used for serial architectures. In this paper, the analysis of the Tricept manipulator’s dexterous workspace, as a function of architectural variables, is provided through the use of a quantitative metric for dexterity. Furthermore, the generality of this metric is also demonstrated by first employing it to analyze a serial manipulator and then comparing it to a parallel manipulator having the same degrees-of-freedom. The paper also proposes a strategy to deal with singularities introduced mathematically by the novel Jacobian formulation.