Stiffness analysis of a 2-DoF over-constrained RPM with an articulated traveling platform

• Stiffness model of over-constrained RPM considering gravitational effects is formulated.
• Wrench/twist mapping models are carried out for the over-constrained property and gravity.
• Stiffness of limbs is computed by deformation superstition principle in local reference frame.
• Compliance of components is denoted by n-DoF (n ≤ 6) spring concerning passive joint.

Driven by the requirements of inter-satellite link antenna for tracking mechanism with two degree-of-freedom (DoF), this paper proposes a 2-DoF over-constrained rotational parallel mechanism (RPM) with an articulated traveling platform and formulates its stiffness model considering gravitational effects. The stiffness modeling is implemented by three steps: 1) Considering the over-constrained property and gravitational effects, twist/wrench mapping models of two R(RU)2 limbs connecting the fixed base and the articulated traveling platform are obtained based upon screw theory. 2) Employing deformation superposition principle, the compliance models of two R(RU)2 limbs in their joint spaces are formulated, of which component compliance is described by n-DoF (n ≤ 6) virtual springs; and 3) by applying deformation compatibility conditions and twist/wrench mapping models into the virtual work equations, the stiffness model of the 2-DoF over-constrained RPM considering gravitational effects is derived. From component, limbs to mechanism, the stiffness modeling process demonstrates their relations with clear physical meaning and unifies performances including kinematic, stiffness, accuracy and dynamics. This approach is verified by commercial FEA software. Finally the stiffness distribution and gravitational effects within prescribed workspace are discussed.