A variational theorem is presented that may be employed for systematically establishing the equations governing the dynamic response of flexible planar linkage mechanisms simultaneously subjected to both mechanical and hygrothermal loadings. This theoretical development is motivated by recent research advocating that high-speed mechanisms should be fabricated in polymeric fibrous composite materials in order to achieve high-performance characteristics. The constitutive behavior of some of these materials is, however, dependent upon the ambient environmental conditions, and hence mathematical models must be developed in order to predict the response of mechanism systems fabricated with these materials. This class of mechanism systems is modeled herein as a set of continua in which elastic deformations are superimposed upon gross rigid-body motions. By permitting arbitrary independent variations of the system parameters for each link, approximate equations of motion, energy balance, mass balance, and boundary conditions may be systematically constructed. As an illustrative example, the derivation of a problem definition for the flexible connecting-rod of a slider-crank mechanism subjected to hygrothermal loading is presented.

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