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Robotics for Creative Practice - Fall 2021

Two Link Kinematics

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Two Link Kinematics¶

Forward Kinematics¶

The Cartesian location of the elbow joint between the links:

→elbow=(L1sinθ1,L1cosθ1)

The Cartesian location of the end point:

→p=→elbow+(L2sin(θ1+θ2),L2cos(θ1+θ2))

Inverse Kinematics¶

Given an endpoint expressed in polar coordinates:

end=(R,θ)

Internal angles can be labeled as follows:

θ=θ1+αβ=π−θ2

Applying the law of cosines and algebra:

R2=L21+L22−2L1L2cosββ=arccosR2−L21−L22−2L1L2

Applying the law of sine and algebra:

Rsinβ=L2sinαα=arcsinL2sinβR

Calculating the joint angles. Note that zero, one, or two solutions may exist.

θ1=θ−αθ2=π−β

Supporting Material¶

  • documentation of our Webots Two-Link Robot Model

  • my Fall 2020 video lecture on Kinematics of the Two-Link Arm

  • SymPy derivation of two-link inverse kinematics two-link-kinematics.py

  • sample Python code for two-link forward and inverse kinematics: two-link-ik.py

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© Copyright 2021, Garth Zeglin. Licensed under CC-BY-4.0. Last updated on 2021-12-02. Created using Sphinx 3.0.4. University legal notice.