Couplings, coupling networks and their graphs

Freedom and Constraint in Coupling Networks

“…In order to use the methods described here for a statics problem, it is necessary to internalize external actions. Essentially, this means treating active couplings [2] (engines, gravitation, motors, muscles, rams) as if they are passive couplings. Alternatively, such active couplings can be thought of as being replaced by equivalent passive couplings [14] to create an overconstrained coupling network.…”

Stability of long combination vehicles

“…The graph has 23 vertices (links) and 31 edges (joints and external forces (P x , P y and P z )). The direct coupling graph (Figure 9) can be represented by the incidence matrix [I] 23×31 (Davies, 1995). The incidence matrix provides the cut-set matrix [Q] 22×30 (Davies, 1995;Erthal, 2010;Moreno et al, 2015Moreno et al, , 2016aMoreno et al, , 2016b for the mechanism, where each line represents a cut graph and the columns represent the joints and the external forces.…”

Planar revolute-coupled kinematic chains in critical configurations and their duals

“…Accurate manufacture will ensure that any actions within N are of low magnitude. It is interesting to note that the actions within planar mechanisms that are attributable to active couplings [15] belong to another screw system, the 4 th special 3-system of screws. These actions, mainly coplanar forces, are created by active couplings [12] that are not present in kinematic chains but are in machinery.…”

“…This paper is concerned with kinematic chains and their duals. It has been argued [15] that a kinematic chain only becomes a mechanism after input and output ports have been identified. So the distinction that has been made [2] between singularities of the first and second kind is not needed in this paper.…”

“…Likewise, a single point contact between two bodies can only transmit a unidirectional force unless there are two such contacts sharing the same common normal. As well as these passive couplings there are active couplings [15] that are capable of transmitting unidirectional force; two examples are gravitational and magnetic couplings. Both are disregarded in this paper: all bodies are assumed to be weightless.…”