A proposal for a formula of absolute pole velocities between relative poles

International audienceIn this paper is proposed a vectorial equation that relates the absolute pole velocities of three moving rigid bodies with a planar motion of general type. From this equation, it is possible to obtain a relation between the pole velocities of the three mathematical points, related between them by the Aronhold-Kennedy Theorem. The formula allows the calculation of one of the pole velocities from the other two, being known the angular velocities and accelerations of the moving bodies. It is applicable regardless of whether the instantaneous centers (poles) are located on physical points on the linkage or not. Illustrative examples of the application of the formula on representative planar linkages are included. In the final section, is discussed a similar concept associating a mathematical point to the curvature centers of a point's path, so called centroma. Index Terms-Pole, pole velocity, curvature center, centroma. Nomenclature A-Geometric point A of moving body i. P-Instantaneous center (pole) of velocity of moving body i with respect to moving body j. u-Absolute pole velocity of P .-Angular velocity of moving body i.-Angular velocity of moving body i relative to moving body j.-Radius of curvature of the fixed centrode of moving body i.-Radius of curvature of the moving centrode of moving body i.-Angular acceleration of moving body i.-Angular acceleration of moving body i relative to moving body j.-Velocity of physical point C.-Centroma of A (mathematical point associated to the centre of curvature of the path of point A). r-Position vector relating points I and J