title: Inverse Kinematics: Calculating the Jacobian
body: <p>I am trying to do inverse kinematics for a serial chain of arbitrarily many links.</p>
  
  <p>In the following <a href="http://www.math.ucsd.edu/~sbuss/ResearchWeb/ikmethods/iksurvey.pdf" rel="nofollow noreferrer">paper</a>, I have found an example for how to calculate the Jacobian matrix.</p>
  
  <pre><code>Entry (i, j) = v[j] * (s[i] - p[j])
  </code></pre>
  
  <p>where:</p>
  
  <blockquote>
    <p><code>v[j]</code> is the unit vector of the axis of
    rotation for joint j</p>
    
    <p><code>s[i]</code> is the position (int world
    coords?) of joint i</p>
    
    <p><code>p[j]</code> is the position (in world
    coords?) of joint j</p>
  </blockquote>
  
  <p>The paper says that this works if <code>j</code> is a rotational joint with a single degree of freedom. But my rotational joints have no constraints on their rotation. What formula do I then want? (Or am I possibly misunderstanding the term "degree of freedom"?)</p>