Question

Consider a three-joint SCARA robot . The coordinate frames are as in Fig. 2. Fig. 1 ABB IRB 910SC robot Fig. 2 Coordinate frames Its DH parameter table is as follows. Fi−1 →Fi ai αi di θi F0→F1 3000161θ1 F1→F2 250 0 0 θ2 F2→F3 0 0 d3 0

A) Find the homogeneous transformation matrix H0 and the coordinate of o in Frame 0. 33√
B) Find θ , θ , and d if the coordinate of the origin o in Frame F is [150+125 3,125+ √12330 150 3, 200]⊤.
C) If the desired value for the joint variable θ1 is 30o, please design a control law for the motor equipped inside the joint such that the joint variable converges to its desired value and sketch the diagram for the control system.

Answer 1

The engineering question is about deriving a homogeneous transformation matrix using Denavit-Hartenberg parameters for a SCARA robot, finding specific joint variables, and designing a control law for angle convergence.

Step-by-step explanation:

This question pertains to the field of robotics within engineering, specifically to the calculation of homogeneous transformation matrices for a SCARA robot using Denavit-Hartenberg (DH) parameters. The first part of the question asks for the calculation of a homogeneous transformation matrix and the coordinates of the origin in Frame 0. The second part requires solving for the joint angles θ1, θ2, and the displacement d3 given the coordinates of the origin in Frame F3. The final part involves designing a control law to adjust the angle θ1 to its desired value, hinting at concepts of control systems in robotics engineering.

The application of DH parameters to find the transformation matrix is a mathematical procedure involving matrices and trigonometry. The design of a control law implicates principles from control theory and dynamics to ensure that the actuator can reach and maintain the desired angle.