Fixedangle

Fixedangle is a term used in geometry, mechanical design, and computer-aided design to denote a constraint that keeps the angle between two elements constant during motion or transformation. The constraint is specified by a target angle θ0 and is applied to pairs of lines, vectors, joints, or surfaces.

Mathematically, if two directions are represented by vectors u and v, a fixedangle constraint requires ∠(u, v) = θ0, which can be expressed using the dot product: u·v = |u||v|cos θ0. In three dimensions, the concept generalizes to the dihedral angle between two planes or to the angle between two rotating links around a common pivot.

In practice, fixedangle constraints appear in mechanical kinematics and computer-aided design (CAD). They are implemented in constraint solvers to maintain a prescribed orientation between components, enabling predictable motion in linkages, robotic arms, or assemblies under load. They can be combined with distance constraints and hinge joints to form complex mechanisms.

Applications include robotics, animation for character rigs where a joint must preserve a given bend, architectural and mechanical CAD where precise angular relationships are required, and the analysis of mechanisms with locked or limited mobility. Related concepts include angle constraints, distance constraints, dihedral angles, and kinematic chains.