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We present a geometric theory of the performance of robot manipulators, applicable to systems with constraints, which m a y be non-holonomic. The performance is quanti ed by a geometrical object, the induced metric tensor, from which scalars may be constructed by i n variant tensor operations to give performance measures. The measures thus de ned depend on the metric structure of con guration and work space, which should be chosen appropriately for the problem at hand. The generality of thisdoi:10.1109/70.563649 fatcat:xsde34lkg5fytfzzf7nrbuiukm