Singularity analysis example

This notebook performs singulariy analysis on a two-link planar manipulator. This notebook assumes that the definitions in "velocity_kinematics_defs.nb" have already been evaluated.

DH parameters (two-link planar manipulator)

DH  =  {{0, 0, 0, θ1, 0}, {0, L1,  0,  θ2, 
            0},  {0,  L2,  0,  0, 0}}; 
DH  // TraditionalForm

Singularity analysis

Compute the Jacobian relating (vx, vy) to (dθ1/dt, dθ2/dt)

j1  =  
        TakeMatrix[Jacobian1[DH, 0, 3], {1, 1},  {2, 2}]  // 
          Simplify;
j1  //  TraditionalForm

|J| (determinant)

Det[j1]  //  TraditionalForm

Simplify[Det[j1]]  //  TraditionalForm