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The paper deals with the motion planning problem for a rolling sphere with limited contact area. The system under consideration is represented by a hemispherical object that can roll without slipping or spinning on the plane. Under the constraints imposed on the size of the contact area, the construction of motion can be regarded as a problem of parallel parking in a finite number of movement steps. A motion strategy, realizing the movement steps by tracing generalized figure eights on the hemisphere, is introduced. Two different algorithms for this motion strategy, the circle-based and the generalized Viviani-curve-based ones, are proposed. The convergence of the algorithms is analyzed, and the computational feasibility of these algorithms is verified under simulation.