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I'm trying to obtain dynamics of a 4 DOF robot. Firstly, I calculated all Transformation matrices and Jacobians. While solving Lagrangian there is a term I - Inertia tensor . I couldn't understand the formula and how it is applied to a link (Because I couldn't find any example of Finding inertia tensor for a link instead they are explaining with ordinary rectangular bar). I wanted to know how to find that Inertia tensor matrix ? So please someone help me

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You can calculate the inertia tensor for some primitive geometries of a linkage using known formula. Most of these are listed here. If you do not have a regular shape for which you can find the inertia tensor by a simple formula, you need to obtain this through integration (using the generalised formula). As this is not practicable by hand, most CAD programs (e.g. SolidWorks, Invetor) can calculate the inertia tensor for you for a CAD model. Care must be taken:

  • Make sure that the inertia tensor is expressed in the coordinate system your dynamical model is expecting it to be expressed in. You can change the coordinate system it is expressed in in the CAD program.

  • Furthermore, care must be taken to make sure the right material (material density) is selected for the model (as this is not required for any other purposes then static/dynamic load and/or deformation calculations it is often neglected leading to incorrect results)

Also, please be advised that due to modelling inaccuracies, the calculated inertia tensor is usually only close to the actual value, it does not exactly equal it. Reasons behind this are modelling inaccuracies (e.g. motors are modelled as a block, instead of a rotor and a stator with exact dimensions, cables, shafts, gearboxes are not modelled correctly, etc.).

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