Experimental Validation of Direct Kinematics of a Passive Stewart–Gough Platform with Modified Cardan Joints Using Integrated Absolute Linear Encoders

This paper presents the experimental validation of a computational kinematic model for a passive Stewart–Gough platform equipped with modified Cardan joints. The introduced joint geometry significantly increases structural stiffness but invalidates the standard spherical joint assumption commonly used in hexapod kinematic formulations. To address this, we develop an efficient numerical optimization based framework that solves both the direct and inverse kinematics without relying on simplified joint models. Furthermore, to enable autonomous and absolute pose measurement, each cylindrical leg joint of the platform is equipped with a LinACE™ absolute linear encoder. This sensor integration transforms the passive mechanism into an IoT-enabled reconfigurable fixture capable of internally sensing, tracking, and recalling its own configuration. The direct kinematics are computed iteratively using a homogeneous-transformation formulation and benchmarked against analytical models derived for ideal spherical joints. Experimental results demonstrate sub-millimeter accuracy in pose estimation, confirming the validity of the proposed kinematic model and highlighting the suitability of the sensor-equipped hexapod for industrial flexible fixturing applications.