This is the first of a series of papers dealing with the path planning for a spatial 4R robot with multiple spherical obstacles inside the workspace. In this paper, a time efficient algorithm has been developed to determine a collision free path for the end effector tip of the robot with a single spherical obstacle inside the workspace. A truncated pyramid and a right circular torus are used to model the nonreachable workspaces of the end effector tip of the robot. The problem of guiding the spatial 4R manipulator while avoiding a spherical obstacle is reduced to moving a point while avoiding a truncated pyramid and/or a right circular torus inside the workspace. The point represents the tip of the end effector of the manipulator. This approach produces an efficient algorithm for determining a collision free path. The algorithm has been successfully developed and implemented in the Silicon Graphics 4D-70GT workstation to verify the results.

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