A parametric model for tetra joints applied to compliant delta robot analysis

Unlike rigid mechanisms, compliant mechanisms offer frictionless motion with enhanced precision in compact designs by deriving their motion from the deflection of flexible elements. The Tetra joint, a class of compliant spherical joints, has garnered significant attention in recent years. However, its unique design-featuring a trapezoidal cross-section and trapezoidal blade flexures-poses significant modeling challenges. This work extends our previous study, where we developed a geometric model for streamlined Tetra joint modeling suitable for implementation in Computer-Aided Engineering (CAE) platforms. In this study, we expand the applicability of this model to the analysis and simulation of complex robotic systems, specifically compliant Delta robots. A compliant Delta robot constructed with Tetra joints, termed DeltaFlex, is numerically and parametrically modeled using the developed geometric model of the Tetra joint. To identify the primary contributors to kinematic errors, a systematic analysis is performed. This methodology combines numerical simulations with statistical correlation analysis to evaluate the relationships between design parameters and system errors. The results reveal that the angle between the two sides of the triangle in the Tetra joint has a dominant effect on system errors. Specifically, smaller angles lead to significantly higher kinematic errors.