Question 5.24: A Single-Link Robot Arm with a Gearbox Consider the single-l...
A Single-Link Robot Arm with a Gearbox
Consider the single-link robot arm in Example 5.20. It is driven by a DC motor through a gearbox with a gear ratio N = 1/70. The mass moments of inertia of the motor and the load are I_m and I, respectively. The coefficients of torsional viscous damping of the motor and the load are B_m and B, respectively. τ_m is the torque generated by the motor. The parameter values are I_m = 3.87 × 10^{–7} \text{kg ⋅ m}^2, I = 0.0016 \text{kg ⋅ m}^2, B_m = 0 \text{N ⋅ m ⋅ s/rad}, and B = 0.004 \text{N ⋅ m ⋅ s/rad}. Assume that the robot arm is initially at rest and the motor torque is τ_m(t) = 0.003u(t), where u(t) is the unit-step function with a step time of 0 seconds. Build a Simscape model of the physical system and find the angular velocity output \dot{θ}(t).
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