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Add a Joint type for modeling the lumbar, thoracic, and cervical spine #4177

@nickbianco

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@nickbianco

The current full-body OpenSim models we distribute (e.g., the Rajagopal model) connect the pelvis and torso using three rotational DOFs (e.g., via a CustomJoint). This is usually sufficient for simulations focused on the lower body, but in generally is a poor approximation of the spine when simulating the full body during highly dynamic movement.

ConstantCurvatureJoint provides one candidate for modeling the spine, but has a few issues. First, it requires internally clamping coordinate values to avoid divide-by-zero errors. Secondly, it is difficult to guarantee a continuous spine, where the end of one segment is connected and tangent to the following segment.

A possible alternative is a joint based on beam bending formulae. Beam bending has a closer connection to the bending of spinal segments and if the joint is based around cantilever beams, then continuity and tangency are guaranteed.

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