Motion Design Considering Moment of Inertia

Abstract

Motion design is an essential step in the application of mechanisms. By minimization of motion parameters, e.g. velocity, acceleration and jerk it is possible to reduce the amplitudes of forced vibrations and deformations due to kinetic forces. This also influences the effective torque needed to drive the mechanism. However the moment of inertia J(φ) of non-linear translating mechanisms depends on the mechanism’s position defined by the generalized coordinate φ. Therefore the general approach of minimizing dynamics parameter velocity and its derivatives is a simplification that does not take into account J(φ). This paper suggests an approach to derive the constraints of the motion parameters from the values of J(φ) and J’(φ). A linear programming approach using harmonic synthesis is used for optimization of the motion parameters. This method also offers the possibility to minimize the excitation of a forced vibration. The resulting drive torque of a 1-DOF mechanism is compared for traditional constant constraints with the suggested approach using a multibody model.