Synthesis of Precision Flexible Mechanisms Using Screw Theory with a Finite Elements Validation
The design of flexible parallel stages has recently been systematized for the three-dimensional space using Screw Theory. This methodology has shown to be practical for precision engineering applications where flexural elements, like beams and blades, are subjected to small displacements; therefore, the statics can be represented by using infinitesimal twists and wrenches. The relationships between the reciprocal twists and wrenches spaces can be related and manipulated by linear algebra. In this work, an analytical enumeration of twists and their associated wrenches for any degree of freedom with zero and infinite pitches is developed. Two synthesis problems are analytically calculated and validated using finite element analysis.
KeywordsPrecision mechanisms Screw Theory Linear algebra Finite element analysis
The authors acknowledge the financial support from the Universidad Tecnológica Nacional (UTN) through project PID-UTN 3935, from the Agencia Nacional de Promoción Científica y Tecnológica PICT-2013-2894, and from Consejo Nacional de Investigaciones Científicas y Técnicas PIP 1105, all from Argentina. We gratefully acknowledge the joint work and friendly assistance of Juan A. Bernad from UTN-FRC, Córdoba, Argentina.
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