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For a joint this becomes a set of equations for the linked degrees of freedom of the form. In the simplest form if the constraint axis of the two nodes are the same

us=upu_{s} = u_{p}

When the constraint axes of the two nodes differ there is an adjustment of the form

us=DsDpTupu_{s} = D_{s}{D_{p}}^{T}u_{p}

Where Ds,DpD_{s},D_{p} are the direction cosines associated with the secondary and primary nodes respectively