A tetrahedron approach for a unique closed‐form solution of the forward kinematics of six‐dof parallel mechanisms with multiconnected joints

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Abstract
This article presents a new formulation approach that uses tetrahedral geometry to determine a unique closed‐form solution of the forward kinematics of six‐dof parallel mechanisms with multiconnected joints. For six‐dof parallel mechanisms that have been known to have eight solutions, the proposed formulation, called theTetrahedron Approach, can find a unique closed‐form solution of the forward kinematics using the three proposed Tetrahedron properties. While previous methods to solve the forward kinematics involve complicated algebraic manipulation of the matrix elements of the orientation of the moving platform, or closed‐loop constraint equations between the moving and the base platforms, the Tetrahedron Approach piles up tetrahedrons sequentially to directly solve the forward kinematics. Hence, it allows significant abbreviation in the formulation and provides an easier systematic way of obtaining a unique closed‐form solution.