Freedom and Constraint in Coupling Networks

Abstract

Kirchhoff's circulation law has previously been adapted for studies of underconstraint. Here Kirchhoff's cutset law is also adapted for studies of overconstraint. The two procedures are presented in tandem to emphasise their duality. The same tasks are then undertaken using dual virtual power methods. One is a new procedure for underconstraint that introduces the concepts of cutset motion and virtual action, dual with previously reported circuit action and virtual motion. Of the four methods described, the superior ones for each task are identified.

Relevance of the hyperelastic behavior of cruciate ligaments in the modeling of the human knee joint in sagittal plane

“…In this section the forces in the cruciate ligaments are calculated by static analysis using the Davies' cutset law [8,9]. The experimental procedure proposed in [7] is modeled and simulated.…”

“…In [11,12] the human knee modeling using Davies' method [8][9][10] was proposed. The static analysis of this work is based on previous works [11,12].…”

“…The static analysis of this work is based on previous works [11,12]. The external force and torque as shown in dark arrows (Figure 4 (b)), must be internalized and replaced with equivalent actions (reactions forces) [8][9][10] between links belonging to the mechanism analyzed, resulting in a constrained chain ( Figure 5 (a)). …”

“…Once the actions are internalized, the action graph called GA ( Figure 5 (b)) is constructed [8], where the 8 edges R x and R y represent the passive actions between each link in 0, 1, 2 and 3, and the edges F and represent the active actions between links 0 and 2.…”

“…The model was developed based on the mechanism theory, the screw theory and the Davies' method [8][9][10]. This model allows us to simulate the positions and forces of a healthy ACL in the sagittal plane, considering the hyperelastic behavior of the cruciate ligaments.…”