Equimomental systems representations of point-masses of planar rigid-bodies

This paper presents a study on the equimomental systems of point-masses of planar rigid bodies. In this work, the equimomental systems of three point-masses of planar rigid bodies are investigated using the concept of pseudo-inertia matrix. It is found that given a planar rigid body, it is always possible to determine an equimomental system of three equal masses located at the vertices of an isosceles triangle. A procedure is presented to determine equimomental systems with different masses, guaranteeing that the masses are positive. It is shown that it is always possible to choose an equimomental system of three point-masses located at the vertices of an isosceles triangle with a prescribed position of one mass. The conditions for prescribing the position of two and three point-masses are also investigated. A first idealized example shows the step-by-step procedure for determining an equimomental system of three point-masses of a planar rigid body. The proposed model is applied to a symmetric connecting rod in a second example due to its wide use in combustion engines. A third example shows an equimomental system of an asymmetric bucket of an excavator.