In general, it is not possible to determine the actual manipulator platform's pose of a parallel mechanism from its active joints' coordinates. This problem is usually solved by using additional numerical procedures or by additional system information from auxiliary sensors, providing several weaknesses including initial pose estimations, reference drives, or workspace limitations. In this paper, we therefore introduce a closed-form solution for the direct kinematics problem of the planar 3-RPR parallel mechanism by using only the orientations of two active joints and the manipulator platform, where P denotes active prismatic joints and R passive revolute joints.

The direct kinematics problem of the Stewart-Gough platform can be solved by measuring the manipulator platform's orientation and two of the linear actuators' orientations instead of the six linear actuators' lengths. In this paper, the effect of measurement errors on the calculated manipulator platform's pose is investigated using the Cramer-Ran lower bound and extensive experiments on a state-of-the-art Stewart-Gough platform. Furthermore, different algorithms and filters for one-time as well as continuous pose determinations are investigated. Finally, possible sensor fusion concepts for the one-time pose determination are presented to increase the robustness against noise and measurement errors.

One of the main tasks in robotics is to precisely connect the robot's coordinate system with the world's coordinate system. For parallel mechanisms, this is a challenging task due to the direct kinematics problem, which is usually solved by using iterative algorithms to search for the mobile platform's position and orientation or by adding auxiliary sensors. In this paper, a sensor concept for solving the direct kinematics problem of the Stewart-Gough platform is presented where only three inertial measurement units are used with the aim to renounce length sensors as well as initial and, in some cases, external pose measurements.