Linear and nonlinear analytical equations for fast design of three types of triangular-amplified compliant mechanisms

Compliant amplification mechanisms based on the triangular principle have attracted considerable applications in precision and other engineering fields due to their compactness and efficient amplification capacity. However, a fast engineering design for geometric nonlinearity of large strokes is still much challenging. We report herein a series of analytical equations of nonlinear amplification ratio, input and output stiffness for three commonly-used triangular-amplified compliant mechanisms, namely the rhombus, diamond and bridge types. The pronounced geometric nonlinearities of axially-loaded stiffening and kinematics-arching effects are explicitly formulated. The proposed nonlinear formulas can be directly degenerated as the linear models by vanishing the nonlinear terms, which enables a comprehensive analysis of linear and nonlinear kinetostatics, and hence offers a straightforward way for the fast performance evaluation and size synthesis/optimization. This relieves an engineer's experience and knowledge for an ab initio modeling process. The prediction error is discussed and some insights into the linear and nonlinear characteristics of the three commonly-used triangular-amplified compliant mechanisms are outlined that confirms the advantage of analytical equations bringing to a fast engineering analysis and design.