I'm trying to obtain dynamics of a 4 DOF robot. Firstly, I calculated all Transformation matrices and Jacobians. While solving Lagrangian there is two main things one is kinetic energy and the other is potential energy . The kinetic energy is simplified into D matrix and Coriolis's factor, which to find the gravitational factor in lagrangian method , we need to find the potential energy. My problem is in that potential energy which is equal to P=mgh . I don't know what does that h correspond to and how to find the value of h . Could some one help me solving this issue ?

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1 Answer 1


The height h is a height relative to some arbitrary baseline. You can set it anywhere you want, but I think typically the easiest way to choose your baseline height is to set zero as the lowest reachable point for your robot. Then all heights are positive and you can have zero kinetic energy when speed is zero and zero potential energy when your arm is at its lowest point.


Based on your graphic, it looks like $F_1$, your first joint, is at the top, so you've drawn the arm with as low of a reach as it could have. That means the $h=0$ datum should be through the center of the bottom joint (or center of mass of the end effector, but you don't have a Frame 5 $F_5$ depicted):

h=0 datum

  • $\begingroup$ Ok but How to find that h value because I saw the value of h in a form of expression with cos and sin thetas . Because we need to differentiate that whole potential energy with respect to (q) for lagrangian formulation where the (q) is available only with that h expression (as cos(q) ,sin(q)) . So can you help me , how to find the value of h ? $\endgroup$ Commented Nov 3, 2020 at 6:36
  • $\begingroup$ @RAKESHKUMARK - Put the arm at its lowest possible position. This becomes the h=0 datum. Then you measure h as the vertical distance from that datum. You'll wind up with whatever expressions are necessary to convert your robot arm's positions to vertical distances. $\endgroup$
    – Chuck
    Commented Nov 3, 2020 at 14:10
  • $\begingroup$ Sorry , Can you explain me in a more elaborate way? This is my first attempt towards Robotics , so kindly help me . The motive is doing dynamics using Lagrangian formulation. In that how to calculate the potential energy ? $\endgroup$ Commented Nov 3, 2020 at 15:47
  • $\begingroup$ @RAKESHKUMARK - If you don't provide any drawings, then no, there's nothing more I can say. Please edit your question to provide a drawing of your arm in its normal state, and in its lowest-reachable condition, and include any joint and linkage labels, datums, polarities, etc. $\endgroup$
    – Chuck
    Commented Nov 3, 2020 at 16:03
  • $\begingroup$ yes , I added my picture . Can u please explain me now how to find potential energy clearly? $\endgroup$ Commented Nov 6, 2020 at 15:25

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