Consider the serial mechanism composed of three joints *J*_{1}, *J*_{2}, and *J*_{3} having joint twists $t1,\u2009t2$, and $t3$, respectively. Since twist $t1$ is reciprocal to wrenches $w2$ and $w3$, *J*_{1} must be at the intersection of the two wrenches. Similarly, joint *J*_{2} must be at the intersection of wrenches $w1$ and $w3$, and joint *J*_{3} must be at the intersection of wrenches $w1$ and $w2$. Therefore, as shown in Fig. 5, the triangle formed by the three line spring axes in the parallel mechanism is coincident with the triangle formed by the three revolute joints in the serial mechanism. We define such a pair of parallel and serial mechanisms as *dual elastic* mechanisms.