By the end of this section, you should be able to

1. Identify actuator and sensor roles in electro-mechanical systems and define the direction of signal conversion

2. Write the governing electrical equations for an armature circuit (KVL and KCL) and the mechanical equation of motion for the load

3. Apply Laplace transforms to the electrical and mechanical equations to move from differential equations to algebraic relations

4. Couple the domains using interface equations, such as back EMF and motor-torque relations

5. Derive transfer functions that map an electrical input (voltage or current) to a mechanical output (angular position or angular velocity)

6. Check the model for consistency by verifying units and sign conventions and confirming that the response matches physical intuition

This section introduces electro-mechanical systems, where electrical circuits and mechanical dynamics are linked in a single model so you can track how signals and energy move across domains. In many real devices, a voltage or current drives motion, and that motion produces forces, displacements, or even a feedback signal back into the circuit. The focus here is building models that connect these pieces cleanly and consistently, using equations that tie electrical variables (voltage and current) to mechanical variables (force, torque, displacement, and velocity). You will practice setting up the coupled governing equations, choosing clear inputs and outputs, and then converting the result into a transfer function that relates what you apply to what you measure. That transfer function becomes the bridge from physical understanding to analysis tools, letting you predict transient response, steady behavior, and the effect of changing parameters without re-deriving everything each time. Use the table of contents below to move through the examples and code resources, and keep an eye on units and sign conventions since cross-domain models fail quickly when those basics are sloppy.