Deterministic design for a compliant parallel universal joint with constant rotational stiffness

Compliant universal joints have been widely employed in high-precision fields due to plenty of good performance. However, the stiffness characteristics, as the most important consideration for compliant mechanisms, are rarely involved. In this paper, a deterministic design for a constraint-based compliant parallel universal joint with constant rotational stiffness is presented. First, a constant stiffness realization principle is proposed by combination of the freedom and constraint topology (FACT) method and beam constraint model (BCM) to establish a mapping relationship between stiffness characteristics and topology configurations. A parallel universal joint topology is generated by the constant stiffness realization principle. Then, the analytical stiffness model of the universal joint with some permissible approximations is formulated based on the BCM, and geometrical prerequisites are derived to achieve the desired constant rotational stiffness. After that, finite element analysis (FEA), experimental testing, and detailed stiffness analysis are carried out. It turns out that the rotational stiffness of the universal joint can keep constant with arbitrary azimuth angles even if the rotational angle reaches up to 65 deg. Meanwhile, the acceptable relative errors of rotational stiffness are within 0.53% compared with the FEA results and 2.6% compared with the experimental results, which indicates the accuracy of the theoretical stiffness model and further implies the feasibility of constant stiffness realization principle on guiding the universal joint design.