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In this paper, the optimum design of parallel kinematic toolheads is implemented using genetic algorithms with the consideration of the global stiffness and workspace volume of the toolheads. First, a complete kinetostatic model is developed which includes three types of compliance, namely, actuator compliance, leg bending compliance and leg axial compliance. Second, based on this model, two kinetostatic performance indices are introduced to provide a new means of measuring compliance over the workspace. These two kinetostatic performance indices are the mean value and the standard deviation of the trace of the generalized compliance matrix. The mean value represents the average compliance of the Parallel Kinematic Machines over the workspace, while the standard deviation indicates the compliance fluctuation relative to the mean value. Third, design optimization is implemented for global stiffness and working volume based on kinetostatic performance indices. Additionally, some compliance comparisons between Tripod toolhead and other two principal Tripod-based Parallel Kinematic Machines are conducted.

In this paper, a new method for optimal calibration of parallel kinematic machines (PKMs) is presented. The basis of the methodology is to exploit the least error sensitive regions in the workspace to yield optimal calibration. To do so, an error model is developed that takes into consideration all the geometric errors due to imprecision in manufacturing and assembly. Based on this error model, it is shown that the error mapping from the geometric errors to the pose error of the PKM depends on the Jacobian inverse. The Jacobian inverse would introduce spurious errors that would affect the calibration results, if used without proper care. Hence, areas in the workspace with smaller condition numbers are selected for calibration. Simulations and experiments are presented to show the effectiveness of the proposed method. Calibration software based on the proposed method has been embedded in the tripod developed at the National Research Council of Canada’s Integrated Manufacturing Technologies Institute.