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

( -L1 sin(θ1) - L2 sin(θ1 + θ2) -L2 sin(θ1 + θ2) ... ) L1 cos(θ1) + L2 cos(θ1 + θ2) L2 cos(θ1 + θ2)

|J| (determinant)

Det[j1] // TraditionalForm

L1 L2 cos(θ1) sin(θ1 + θ2) - L1 L2 cos(θ1 + θ2) sin(θ1)

Simplify[Det[j1]] // TraditionalForm

L1 L2 sin(θ2)

Created by Mathematica  (October 1, 2003)