Manipulators consisting of multiple large deformation limbs can flexibly change their shapes and separate actuation systems from mechanism body, making them particularly suitable for requirements of compact design space, and continuous and versatile deformation. However, the low structural stiffness restricts their practical applications. To enhance the stiffness, we have integrated lockable variable geometry truss (LVGT) supports within the manipulator design. Depending on the number of locked branches within the LVGT, the active flexible limbs may exhibit redundant actuation modes, meaning that the number of working actuators exceeds the DOF of the internal LVGT. The redundant actuation modes, while beneficial for enabling heavier load manipulation, poses challenges in mechanical analysis, necessitating a comprehensive consideration of factors such as motion constraints from rigid joints, nonlinear coupling deformations in the flexible limbs, and control strategies for the redundant actuators. In this paper, we construct a mechanical analysis framework tailored for such operating modes. This framework enables the kinetostatic analyses under the consideration of distributing redundant actuation forces.