I am aware of various different approaches of kinematic modelling of parallel mechanisms. I have currently employed the vector loop closure equations to solve the inverse kinematics problem. The problem is, the vector loop closure method eliminates the passive joint variables. I need to see how these are behaving while I proceed with dynamic modelling. Are there any textbook methods that are capable of estimating all the joint variables? (active + passive)

  • $\begingroup$ What structure of the parallel mechanism is used in your project? $\endgroup$
    – ayr
    Commented May 7, 2020 at 10:08
  • $\begingroup$ It is a novel mechanism, of 1T2R type motion pattern. The limbs are connected to the moving platform using spherical joints. While using the vector loop method, these are eliminated from the picture. But I would like to know how the passive joint variable values. $\endgroup$
    – isaac john
    Commented May 7, 2020 at 14:23
  • $\begingroup$ I approximately represent your difficulties with using a vector loop closure equations when working with passive joints. Check out this article, will it be useful to you? Modeling and Analysis of a 2-DOF Spherical Parallel Manipulator $\endgroup$
    – ayr
    Commented May 8, 2020 at 8:52
  • $\begingroup$ Thanks for the help. The difficulty was that the passive joint variables are eliminated from the kinematic model. My aim is to incorporate passive joint variables into the kinematic model as well. I was hoping for a textbook methodology like DH method. I think there are no such general methodologies available at present. That leaves me with no choice other than exploiting the mechanism's geometry and constraints. $\endgroup$
    – isaac john
    Commented May 8, 2020 at 14:13

1 Answer 1


After you calculate the joint angles, you can go back to each kinematic chain connecting the platforms ans solve the "inverse kinematic problem" of the kinematic chain only.

The base frame of the chain has known coordinates, the end of the chain should have known coordinates and the already calculated active joint angle can be used to reduce the number of unknowns.

  • $\begingroup$ Thank you very much. I can use the well known DH modelling for estimating the rest of the joint variables. $\endgroup$
    – isaac john
    Commented May 13, 2020 at 12:52
  • $\begingroup$ Please consider accepting the answer, when it was correct $\endgroup$
    – 50k4
    Commented May 13, 2020 at 13:03

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