CE1.3a Figure 1.16 shows a single robot joint/link driven through a gear ratio n by an armature-controlled de servomotor. The input is the de armature voltage vA(1) and the output is the load-shaft angle OL(1). Derive the mathematical model for this system; i.e., develop the circuit differential equation, the electromechan- ical coupling equations, and the rotational mechanical differen- tial equation. Eliminate intermediate variables and simplify; it will be convenient to use a transfer-function approach. Assume the mass-moment of inertia of all outboard links plus any load JL(1) is a constant (a reasonable assumption when the gear ratio n = Wm/wr is much greater than 1, as it is in the case of industrial robots). The parameters in Figure 1.16 are summarized below. CE1.3b Derive a valid state-space description for the system of Figure 1.16. That is, specify the state variables and derive the ww by JM (1) FIGURE 1.16 Diagram for Continuing Exercise 3. VA(1) armature voltage ia(1) armature current JM kT armature inductance R armature resistance vg (1) back emf voltage bM wM(1) motor shaft velocity L(1) load inertia On (1) load shaft velocity back emf constant kB TM(1) motor torque motor inertia motor viscous damping OM(1) motor shaft angle load viscous damping torque constant gear ratio L(1) load shaft torque OL(1) load shaft angle coefficient matrices A, B, C, and D. Write out your results in matrix-vector form. Give the system order and matrix-vector dimensions of your result. Consider two distinct cases: i. Single-input, single-output: armature voltage VA (1) as the input and robot load shaft angle OL(1) as the output. ii. Single-input, single-output: armature voltage VA(1) as the input and robot load shaft angular velocity wr(t) as the output.

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Motor Load, Torque, and Power Quality Requirement

An electric motor is a gadget that changes electrical energy into mechanical energy over to follow up on a mechanical burden. The weight set on the motor because of this mechanical movement is known as motor load. Appropriately matching the motor burden to the engine is vital to forestall harm to the engine or wasteful and unnecessary expensive activity. Engines perform such undertakings as moving a thing starting with one spot then onto the next, cutting it, changing its shape, etc. The motors might be evaluated as far as a few variables including power yield, voltage, current, and temperature. Harm to an engine might happen when it is worked under over the top engine load contrasted with its appraised limit.