This paper presents a mathematical model of a device we call a 'harmonic motor'. The unit is essentially an acutator based on a harmonic drive gear train, which uses a proper system of forces applied directly to the deformable gear, to control gear deformation and operate the gear train. The actuator potentially performs extremely well: it has fast dynamic response, backlash recovery, continuous (non-stepping) rotation, compact design and high specific torque. However, in order to achieve these features, deep understanding of the principle of operation is required and a suitable control strategy must be formulated. This paper aims at provding a suitable mathematical model. The kinematics of the deformable harmonic gear is based on fourier series expansions of the gear displacements, the coefficients of which form a set of lagrangian coordinates for the gear. A set of equations are then derived to link the input system of forces to the mesh reactions and on the output torque (thus linking input and output quantities). This set is composed of a number of equations describing the motion of the harmonic gar equal to the number of terms in the fourier expansions, plus another three equations describing the mesh constraints and two additional equations for the driven link (one of which describes the torsional compliance of the harmonic gear). A simplified dynamic model with two degrees of freedom is the derived from the complete model by retaining only the two dominant terms from the Fourier approximation of harmonic gear deformation. This simplified model provides remarkably information about the system's behaviour and can also suggest how to control the system to achieve the above performance features.
A mathematical model for harmonic motors
Mathematisches Modell eines 'harmonischen Motors'
1994
8 Seiten, 4 Bilder, 3 Quellen
Conference paper
English
A mathematical model for harmonic motors
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