Singularity Analysis of Redundant Space Robot with the Structure of Canadarm2

Figure 1

A general model of free-floating space robot. Σ_𝐼,Σ_𝐸: the inertia frame and the end-effector frame, respectively. Σ_𝑖(𝑖=1,…,𝑛): the frame of link 𝑖. 𝐶_𝑖(𝑖=1,…,𝑛): the mass center position of link 𝑖. 𝐽_𝑖(𝑖=1,…,𝑛): the position of joint 𝑖. 𝑎_𝑖,𝑏_𝑖(𝑖=1,…,𝑛): the position vectors from𝐽_𝑖to𝐶_𝑖and𝐶_𝑖to𝐽_𝑖+1, respectively. 𝑟_𝑖(𝑖=1,…,𝑛): the position vector of𝐶_𝑖. 𝑟_𝑔: the position vector of the system’s mass center. 𝑝_𝑖(𝑖=1,…,𝑛): the position vector of𝐽_𝑖. 𝑝_𝑒: the position vector of the end-effector. Θ: the joint angle vector. 𝑚_𝑖(𝑖=1,…,𝑛): the mass of link 𝑖. 𝑀: the total mass of the system. 𝐄₃: 3×3identity matrix.