The Atlas platform represents a novel six degree-of-freedom motion platform architecture. Orienting is decoupled from positioning, and unlimited rotations are possible about every axis. The decoupling is accomplished by fixing a three degree-of-freedom spherical orienting device, called the Atlas sphere, on a gantry with three orthogonal linear axes. The key to the design is three omni-directional wheels in an equilateral arrangement, which impart angular displacement to a sphere, providing rotational actuation. The free-spinning castor rollers provide virtually friction-free motion parallel to each omni-wheel rotation axis creating the potential for unconstrained angular motion. Since the sphere directly contacts the omni-wheels, there are no joints or links interfering with its motion, allowing full 360° motion about all axes. However, the kinematic constraints are non-holonomic. This paper explores the slip at the interface between each omni-wheel and the Atlas sphere. A kinematic slip model is presented, introducing the slip ratio, which is the ratio of the kth omni-wheel's transverse velocity component, S⊥k, which is perpendicular to the free-spinning castor wheel axis, and the tangential velocity component, Stank, which is perpendicular to the omni-wheel driving axis, parallel to the tangential velocity vector, Vk. The long-term goal is to incorporate the slip model into a control law for position level control of the sphere. Two illustrative examples are given.

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Journal Transactions of the Canadian Society for Mechanical Engineering
Holland, J.B. (J. B.), Hayes, M.J.D, & Langlois, R.G. (2005). A slip model for the spherical actuation of the atlas motion platform. In Transactions of the Canadian Society for Mechanical Engineering (Vol. 29, pp. 711–720).