Jacobian mapping examples

This notebook simulates inverse velocity mappings for simple two- and three- link planar manipulators, and assumes that the notebook "velocity_kinematics_defs.nb" has already been evaluated. In Section 1 we simulate the inverse velocity relationship  Overscript[θ, .] = J^(-1) Overscript[X, .] for a non-singular circular end-effector path and  for a singular, straight-line end-effector path for a two-link planar manipulator. In Section 2 we simulate some inverse velocity relationships for a three-link planar manipulator; specifically,  Overscript[θ, .] = J^T(J J^T)^(-1) Overscript[X, .], where J relates (v_x, v_y)to (θ_1, θ_2, θ_3), and Overscript[θ, .] = J^(-1) Overscript[X, .], where  J relates (v_x, v_y, ω_z)to (θ_1, θ_2, θ_3). In both cases the specified straight-line trajectories result in singularities. Finally, in Section 3 we illustrate the use of Δθ = J^T . ΔXfor iteratively computing the inverse kinematics of a robot manipulator

Section 1: Two-link planar manipulator

Section 2: Three-link planar manipulator

Section 3: Iterative inverse kinematics using Jacobian transpose

Created by Mathematica  (October 1, 2003)