English: Diagram of variables for the universal joint. The axis of axle 1 is perpendicular to the red plane and the axis of axle 2 is perpendicular to the blue plane, which are at an angle β with respect to each other. The angular displacement of each axle is given by ${\displaystyle \gamma _{1}}$ and ${\displaystyle \gamma _{2}}$ respectively, which are the angles of the unit vectors ${\displaystyle {\hat {x}}_{1}}$ and ${\displaystyle {\hat {x}}_{2}}$ with respect to their initial positions along the x and y axes respectively. The ${\displaystyle {\hat {x}}_{1}}$ and ${\displaystyle {\hat {x}}_{2}}$ vectors are fixed in the gymbal which connects the two joints and so are constrained to remain perpendicular to each other at all times.