Hinge Joint Theory
The Hinge Joint, also known as a revolute joint, has one rotational degree of freedom between the two components. The two components are free to rotate relative to each other about the axis of the joint.
The following is an addition to the Prismatic Joint Theory, some of which is also applicable for the hinge joint.
Hinge Joint axis and its local coordinate system
In 2D, the initial joint axes (e10, e20, and e30) are always global spatial axes with the initial joint axis (e10) being the out-of-plane axis (ez):
Hinge Joint Formulation
For a hinge joint, the destination attachment is free to rotate relative to the source attachment about the joint axis. The relative rotation about the joint axis (θ) is the degree of freedom.
To formulate this kind of connection, the motion of the destination attachment is prescribed in terms of the motion of the source attachment with the following relations:
The relative quaternion in the global spatial coordinate system (ar, br) is defined as:
In 2D, the motion of the destination attachment is prescribed in terms of the motion of the source attachment by:
Joint Elasticity in Hinge Joint
The elastic degrees of freedom are written as