We present an analytical model for characterizing the motion trajectory of an arbitrary planar compliant mechanism. Model development consists of identifying particular material points and their connecting vectorial lengths in a manner that represents the mechanism topology; whereby these lengths may extend over the course of actuation to account for the elastic deformation of the compliant mechanism. The motion trajectory is represented within the model as an analytical function in terms of these vectorial lengths, whereby its Taylor series expansion constitutes a parametric formulation composed of load-independent and load-dependent terms. This adds insight to the process for designing compliant mechanisms for high-accuracy motion applications because: (1) inspection of the load-independent terms enables determination of specific topology modifications that reduce or eliminate certain error components of the motion trajectory; and (2) the load-dependent terms reveal the polynomial orders of principally uncorrectable error components in the trajectory. The error components in the trajectory simply represent the deviation of the actual motion trajectory provided by the compliant mechanism compared to the ideally desired one. A generalized model framework is developed, and its utility demonstrated via the design of a compliant microgripper with straight-line parallel jaw motion. The model enables analytical determination of all geometric modifications for minimizing the error trajectory of the jaw, and prediction of the polynomial order of the uncorrectable trajectory components. The jaw trajectory is then optimized using iterative finite elements simulations until the polynomial order of the uncorrectable trajectory component becomes apparent; this reduces the error in the jaw trajectory by 2 orders of magnitude over the prescribed jaw stroke. This model serves to streamline the design process by identifying the load-dependent sources of trajectory error in a compliant mechanism, and thereby the limits with which this error may be redressed by topology modification.

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