A Proposal for a Formula of Absolute Pole velocities between Relative Poles

Post-PrintIn 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.The authors wish to acknowledge the financial support received from the Spanish Government through the "Ministerio de Economía y Competitividad" (Project DPI2015-67626-P (MINECO/FEDER, UE)), the financial support from theUniversity of the Basque Country (UPV/EHU) under the program UFI 11/29 and the support to the research group, through the project with ref. IT949-16, given by the "Departamento de Educación, Política Lingüística y Cultura" of the Regional Government of the Basque Country