Analytical Modeling and Validation of New Prismatic Compliant Joints Based on Zero Poisson’s Ratio Lattice Structures

The design and analysis of prismatic compliant joints have received less attention compared to that given to revolute compliant joints, thus limiting their implementation in compliant mechanisms beyond translational stages. Lattice structures have been used effectively to increase flexibility and stiffness ratios in compliant joints. Considering these, new prismatic compliant joints based on zero Poisson’s ratio lattice structures (ZP-PCJ) are proposed. Lattices with three different cell arrangements are considered: single cells, $2×2$⁠, and $3×3$ lattices. Additionally, unit cells with three different geometries are studied: triangular, chamfer, and cosine. The compliance matrices of the ZP-PCJs are assembled analytically using Castigliano’s second theorem and compliance series–parallel simplification. The compliance ratios along the three orthogonal axes of the ZP-PCJs are computed varying their geometric parameters. Finite element models are constructed to validate the analytical results. Experimental tests are performed on additively manufactured ZP-PCJs to corroborate the compliance coefficients. Results showed that analytical models can predict the ZP-PCJ’s elastic properties accurately, differences less than 3% and 12% were obtained when compared to computational and experiments, respectively. Based on the compliance ratios obtained, the ZP-PCJs are suitable for two-dimensional applications. Finally, the ZP-PCJs are implemented in a compliant mechanism to evaluate their behavior, analytically and computationally. The ZP-PCJs have advantages such as eliminating axis drift and high flexibility in motion-direction while maintaining stiffness in other directions. The differences observed when comparing the analytically obtained estimations with simulations and experimental data suggest that ZP-PCJ analytical models are reliable for estimating their performance in compliant systems.