A Single-Link Robot Arm with a Gearbox Consider the single-link robot arm in Example 5.17. It is driven by a DC motor through a gearbox with a gear ratio of N = 1/70. The mass moments of inertia of the motor and the load are Im and I, respectively. The coefficients of torsional viscous damping of

Question

A Single-Link Robot Arm with a Gearbox

Consider the single-link robot arm in Example 5.17. It is driven by a DC motor through a gearbox with a gear ratio of [latex]N=1 / 70[/latex]. The mass moments of inertia of the motor and the load are [latex]I_{\mathrm{m}}[/latex] and [latex]I[/latex], respectively. The coefficients of torsional viscous damping of the motor and the load are [latex]B_{\mathrm{m}}[/latex] and [latex]B[/latex], respectively. [latex] au_{\mathrm{m}}[/latex] is the torque generated by the motor. The parameter values are [latex]I_{\mathrm{m}}=3.87 imes[/latex] [latex]10^{-7} \mathrm{~kg} \cdot \mathrm{m}^{2}, I=0.0016 \mathrm{~kg} \cdot \mathrm{m}^{2}, B_{\mathrm{m}}=0 \mathrm{~N} \cdot \mathrm{m} \cdot \mathrm{s} / \mathrm{rad}[/latex], and [latex]B=0.004 \mathrm{~N} \cdot \mathrm{m} \cdot \mathrm{s} / \mathrm{rad}[/latex]. Assume that the robot arm is initially at rest and the motor torque is [latex] au_{\mathrm{m}}(t)=0.003 u(t)[/latex], where [latex]u(t)[/latex] 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 [latex]\dot{ heta}(t)[/latex].

Accepted Answer

The Simscape model of the system is shown in Figure 5.114. To model the robot arm, two Inertia blocks are included, one for the motor and the other for the load. Because the damping of the motor can be ignored, one Rotational Damper block is included to represent the damping of the load. The shaft of the motor and that of the load are coupled through a gearbox. Double-click on the Gear Box block and type 70 (not 1/70) for the Gear ratio, which in Simscape is defined as the ratio of the input shaft angular velocity to that of the output shaft. This is the reciprocal of the gear ratio defined in Equation 5.53.

[latex] \frac{\omega_2}{\omega_1} = N.[/latex] (5.53)

The output of port [latex]\mathrm{W}[/latex] of the Ideal Rotation Motion Sensor is the corresponding angular velocity [latex]\dot{ heta}(t)[/latex], which is shown in Figure 5.115.

Note that only the Simscape block diagrams are given in the above two examples. The corresponding Simulink modeling is left to the reader as an exercise.

Question 5.21: A Single-Link Robot Arm with a Gearbox Consider the single-l...

Related Answered Questions

Verified Answer:

A Two-Degree-of-Freedom Mass–Spring System Consider the two-degree-of-freedom mass–spring system shown in Figure 5.106. The mathematical model of the system is given by a set of ordinary differential equations m1x1 + (k1 + k2)x1 – k2x2 = 0, m2x2 – k2x1 + k2x2 = 0, where m1 = m2 = 5 kg, ...

Verified Answer:

Verified Answer:

Verified Answer:

A Single-Degree-of-Freedom Gear–Train System For the gear–train system shown in Figure 5.95a, derive the differential equation of motion. The mass moments of inertia of the two gears about their respective fixed centers are IC1 and IC2. ...

Verified Answer:

Verified Answer:

Verified Answer:

A Cart–Inverted-Pendulum System Consider the mechanical system shown in Figure 5.79, in which a uniform rod of mass M and length L is pivoted on a cart of mass m. An external force f is applied to the cart. Assume that the pendulum is constrained to move in a vertical plane, and the cart moves ...

Verified Answer:

Verified Answer:

A Pure Rolling Disk Consider the system shown in Figure 5.60a, in which a uniform disk of mass m and radius r rolls on a horizontal surface. A translational spring of stiffness k is attached to the disk. Assuming that there is no slipping between the disk and the surface, derive the differential ...

Verified Answer: