A new global isotropy index (GII) is proposed to quantify the configuration independent isotropy of a robot's Jacobian or mass matrix. A new discrete global optimization algorithm is also proposed to optimize either the GII or some local measure without placing any conditions on the objective function. The algorithm is used to establish design guidelines and a globally optimal architecture for a planar haptic interface from both a kinematic and dynamic perspective and to choose the optimum geometry for a 6-DOF Stewart Platform. The algorithm demonstrates consistent effort reductons of up to six orders of magnitude over global searching with low sensitivity to initial conditions.

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Good robot performance often relies upon the selection of design parameters that lead to a well conditioned Jacobian or impedance "design" matrix. In IntroductionMany robot design variables such as structure (serial vs. parallel), geometry, actuators (rotary vs. prismatic) and reduction ratios contribute to the way a robot behaves. Unfortunately, any change that enhances one performance attribute will almost always detract from another. Stiffness, for example, is improved by using a parallel robot instead of a serial robot but workspace size suffers. This trade-off that occurs with virtually every design variable suggests that a universally optimum device does not exist. Optimality only exists in the context of a specific application since different applications make different performance demands. This paper describes how a robot can be designed for a particular application by integrating application specific performance requirements into the performance function. It shows how to specify desired relative capabilities with respect to individual workspace dimensions and how to improve the solution through asymmetric actuation. The technique also normalizes physical units to ensure a meaningful result. o r m a l i z e t h e J a c o b i a n b y d iv i d i n g a "Characteristic Length" (CL) out of all translational elements. The CL that produces the best performance measure is dubbed the "Natural Length" (NL) by Ma and Angeles [8] and is used for design optimization. When the NL of a platform manipulator is not derivable, it is approximated by the average platform radius. Angeles [1] calculates the NL for a serial manipulator by averaging the distances between the operating point and all active joint axes while Angeles et. al.[2] find a serial manipulator's NL by making it a free design parameter.It is shown here that the CL, in fact, represents a robot's relative capability to translate and rotate its end-effector. It should be chosen to best satisfy the demands of the application and should not be a free design parameter. The CL is extended to a more general diagonal matrix which scales all workspace dimensions, not just those with dissimilar physical units. A similar type of scaling is also applied to joint-space to simultaneously remove mixed physical units that appear when dissimilar types of actuators are used (e.g. the Stanford Arm) and improve isotropy through asymmetric actuation. Section 2 of this paper discusses the definition of isotropy and the optimization algorithm used in subsequent design examples. Section 3 describes the proposed scaling matrices that are the focus of this paper. The task-space scaling matrix and its relationship with the CL is described in Section 4 while the joint-space scaling matrix is described in Section 5 with a summary and conclusions in Section 6. Isotropy and OptimizationMany different relationships are used to quantify robot performance. They include, but are not limited to, the Jacobian J(x) (1) that relates actuator velocity to endeffector velocity , its tran...

A coarse-jne approach to the design of highfidelity haptic interfaces is proposed based on prior work and new psychophysics studies. The approach involves a finemotion six-degree-of-freedom parallel Lorentz actuator mounted on a seriedparallel coarse-motion stage and coupled through a compliant transmission. The frequency response of a simplified model is used to illustrate the advantages of the approach. The workspaces of three coarse-motion platforms are compared. A novel twinelbow manipulator with all but one of the drive motors in the base is proposed for its simplicity and large workspace size.