GEOMETRICAL METHODS TO LOCATE SECONDARY INSTANTANEOUS POLES OF SINGLE-DOF INDETERMINATE SPHERICAL MECHANISMS

Abstract: A single-degree-of-freedom (DOF) indeterminate spherical mechanism is defined as a mechanism for which it is not possible to find all the instantaneous poles by direct application of the Aronhold-Kennedy theorem. This paper shows that a secondary instantaneous pole of a two DOFs spherical mechanism lies on a unique great circle instantaneously. Using this property, two geometric methods are presented to locate secondary instantaneous poles of indeterminate single DOF spherical mechanisms. Common approach of the methods is to convert a single DOF indeterminate spherical mechanism into a two DOFs mechanism and then to find two great circles that the unknown instantaneous pole lies on the point of intersection of them. The presented methods are directly deduced from a work done for indeterminate single DOF planar mechanisms. Key Words: instantaneous poles, geometrical techniques, indeterminate single-dof spherical mechanism