The next equality constraint we will derive is the prismatic constraint. A prismatic constraint is like the line constraint except it does not allow rotation about the anchor point. A prismatic constraint constraints the linear motion of the bodies along a line. An example of a prismatic joint is the slide of a semi-automatic pistol. The slide is moved back to charge the weapon, then released to its original position. The slide cannot rotate about the pistol, nor can it move up/down or left/right only along one axis.

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The next equality constraint we will derive is the line constraint. A line constraint is like a prismatic constraint (which will most likely be the next post) except allows rotation about the anchor point. A prismatic constraint constraints the linear motion of the bodies along a line. An example of a prismatic joint might be a roller coaster on the track. The cars cannot translate or rotate except along the track. For simplicity the prismatic constraint we will define is only for straight lines.

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The next equality constraint we will derive is the weld constraint. A weld constraint can be used to join two bodies at an anchor point in which the bodies must move and rotate together (all DOF are constrained).

This post will differ slightly from the previous posts. A weld joint is basically a revolute joint + an angle joint. In that case we can use the resulting Jacobians from those posts to skip a bit of the work.

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The next equality constraint we will derive is the angle constraint. An angle constraint can be used to join two bodies forcing them to have the same rotation. This particular constraint will be added to other constraints (in later posts) to form more complex constraints.

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The next equality constraint we will derive is the pulley constraint. A pulley constraint can be used to join two bodies at a fixed distance. In addition, the constraint can be used to simulate a block-and-tackle.

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