A new forward kinematic algorithm for a general Stewart platform

• We proposed an algorithm of forward kinematics for the unsolved 6-6R parallel manipulator.
• The proposed algorithm including 174 geometric parameters was considered in total.
• The model was more accurate than the model containing only 42 geometric parameters.
• The influence of the geometric parameters on the moving platform's pose was analysed.

In this paper, a new forward kinematic algorithm based on dual quaternion for a six-degree-of-freedom (DOF) general Stewart Platform is proposed. The algorithm is established after taking into account the pose parameters of joints and the D–H parameters of each branch chain, which yields a precise mathematic model with a total of 174 geometric parameters. The validity of the algorithm is tested using an inverse kinematic algorithm of a general serial manipulator. The forward kinematic algorithms for the 6-6R and 6-2RP3R mechanisms can be expressed by a unified mathematic model. The proposed algorithm can solve the difficult problem of forward kinematics for the unsolved 6-6R parallel manipulator and can also be applied to error analysis, error synthesis, kinematic calibration, stiffness analysis and the accurate kinematic simulation by analysing the effect of geometric parameters on the platform.