Lagrange multipliers turn joint forces into outputs

Lagrange multipliers make hidden joint forces visible.

In a constrained multibody system, the equations solve motion and constraint reactions together. The multipliers are not bookkeeping artifacts; they are the forces and torques required to enforce the joints.

That matters because a simulation should not only answer “where does it move?” It should also answer “what loads does the mechanism create?”

Related:

• Programatic Mechanisms
• 2D Kinematics and Dynamics
• The physics of Mechanisms in the SPACE