Abstract

The presence of compliant members in a mechanism makes the determination of its degrees-of-freedom out of reach of the traditional Grübler’s formula, as this formula does not account for the additional mobility allowed by compliance. Recent research efforts have led to a generalization of Grübler’s formula that encompasses compliant mechanisms as well. The objective of this work is to apply the formula to a set of practical compliant devices, and further clarify and simplify the approach. This is accomplished as follows: i) The concept of “virtual rigid segments” is introduced to facilitate the identification of the segment compliance of distributed segments with forces applied to them. ii) The motion of compliant devices is interpreted by identifying the inputs equal in number to the calculated possible degrees of freedom. iii) A wide variety of case studies are presented to illustrate the method of application and the value of the approach.

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