Download Flexible Joint

Figure 3 - Flexible Joint - Stationary
Figure 4 - Flexible Joint - Moving
Figure 3 above depicts the joint at rest while Figure 4 depicts the joint at a given α. Notice
that spring #1 has been compressed and spring #2 has been stretched (with respect to
the joint's stationary state). We shall begin by deriving the lengths of each spring in
Figure 4.
L 1x =r−Rsin 
L 1y =Rcos −d
L 2x =rRsin 
L 2y =L 1y =Rcos −d
L 1= L 21x L 21y
2
[3.1]
2
L 2= L 2x L 2y
Next we will derive the force acting on each spring:
F 1=K L 1−LF r
F 2=K L 2−L F r
L
L
F 1x =F 1 1x , F 1y =F 1 1y
L1
L1
L
L
F 2x =F 2 2x , F 2y =F 2 2y
L2
L2
[3.2]
* Fr is the restoring force on each spring. The springs supplied come pre-loaded meaning
they will not stretch before the force Fr is applied.
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Revision: 01