iTwoLink_abg.tex

MTT command:

mtt iTwoLink abg tex

Figure 10.1: System iTwoLink: acausal bond graph

The acausal bond graph of system iTwoLink is displayed in Figure 10.1 (on page ) and its label file is listed in Section 10.1.1 (on page ). The subsystems are listed in Section 10.1.2 (on page ).

This example illustrates the inversion of two link manipulator dynamics using two identical simple mass-spring-damper systems as specification systems.

The velocities $\omega_1=\omega_2$ specified by the specification systems are given in Figure (on page ) together with the input defined in Section (on page ). The torques $\tau_1$ and $\tau_2$ required to give the these velocities specified by the specification system are given in Figures (on page ) and (on page ) respectively.

The corresponding velocity/torque diagrams for joints 1 and 2 appear in Figures (on page ) (on page ) respectively. Such diagrams can be used for actuator sizing in terms of torque, velocity and power.

This non-linear system can be linearised (about the various configurations) and small-signal frequency response methods applied. For example, the four transfer functions $G_11$ to $G_22$ in Section (on page ) (representing the system linearised about zero angles and velocities), give the small-signal relations between the two spec. torques and the required system torques. Used together with $G_31$ and $G_42$ (relating the spec. torques and the joint velocities) gives, in principle, a method for evaluating actuator requirements (for small signals) as a function of frequency.