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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As a follow up post to the Distance Constraint post, we can also create a maximum distance constraint using the same solution we found in the Distance Constraint post. The previous solution created a fixed length distance constraint which forced a pair of bodies to be a given length apart. We can simply add an Read more about Max Distance Constraint[…]

The next equality constraint we will derive is the distance constraint. A distance constraint can be used to join two bodies at a fixed distance. It can also be used as a spring between two bodies.
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As the first entry after the Equality Constraints post, we will perform the derivation of the Point-to-Point constraint, which models a Revolute Joint, in 2D.
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After the first release of the dyn4j project, I felt that it would be good to pass along what I learned about constrained dynamics.

This is not an easy subject and aside from purchasing books there’s not much information out there about it for those of us not accustomed to reading research papers or theses.

In this post I plan to solve a velocity constraint generally. Later posts will be for the individual types of constraints.
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