A new method for the planning of the position and orientation of an end‐effector along a spline path in Cartesian space is presented. The method is developed using parallel computation. This parallel algorithm for path planning is a function of Cartesian displacement which is determined by the system's speed profile. In positional path planning, the algorithm interpolates a spline path directly based on thecircular arc generation methodinstead of composing piecewise‐straight line segments. In rotational path planning, the algorithm eliminates thewobbling approach vectorwhich conventional methods had suffered. When initial data is determined, position and orientation of the end‐effector can be computed in parallel. If the algorithm is executed by three processors, the computational time is reduced by a factor of 1.67. For four and eight processors, the computational time is further reduced by a factor of 2.0 and 2.22, respectively. When the straight line case of the scheme is executed serially, the computing time is about two thirds of that of the conventional method. An example implemented in a UNIX system shows that the algorithm elegantly solves the problem of the wobbling approach vector.