This paper presents a novel algorithm for six-degree-of-freedom (6-DOF) haptic rendering, providing a fast, stable and precise virtual assembly. This algorithm simplifies large and complex CAD models into simple geometric primes, to accelerate the collision detection and therefore the refresh rate. Analytic approach is employed to simulate the virtual assembly. The common assembly process is decomposed into two basic types of manipulations, axis-alignment assembly and face-mating assembly. Some special assembly features (thread, spline and gear, etc) are described in special parameters. The algorithm has been implemented and interfaced with a 6-DOF PHANToM Premium 3.0. We demonstrate its performance on force display of the mechanical assembly. The object with low clearances can be assembled, and the continuous feedback force can be guaranteed at a constant frequency of 1 kHz.

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