Singularity Spotter¶

Run the Singularity Spotter MicroSim Fullscreen

You can include this MicroSim on your website using the following iframe:

<iframe src="https://dmccreary.github.io/robot-arm/sims/singularity-spotter/main.html"
        height="627px" width="100%" scrolling="no"></iframe>

Description¶

Bend the elbow of a two-link arm and watch the determinant fall, the condition number climb and the joint speeds grow as the arm straightens or folds. Then classify eight elbow angles as safe, near a singularity, or singular, from the size of sin(theta2). Used in Chapter 12.

The arm has links of 0.116 m and 0.135 m, and its shoulder stays at 20 degrees. The determinant of its Jacobian is l1 × l2 × sin(theta2). The classes use the size of sin(theta2), written |sin θ2|:

Singular: below 0.02
Near a singularity: from 0.02 up to 0.3
Safe: 0.3 or more

The limits 0.02 and 0.3 are teaching thresholds chosen for this MicroSim. A real program would set its own limits.

Lesson Plan¶

Grade level: Middle school and up (age 12+). Time: 10 to 15 minutes.

Explore. Start at 90 degrees and move the slider slowly toward 0. Read the joint speeds at 90, 10 and 1 degrees. What happens to them?
Try the other end. Move the slider to 170 and then to 180 degrees. A folded arm is singular too.
Try a negative angle. Compare -5 degrees with +5 degrees. Only the size of the sine matters.
Eight angles. Choose Eight angles in the menu. For each angle, work out |sin θ2| with a calculator and press the class it belongs to. Pressing a button commits your answer. You get one attempt at each, and 7 of 8 is mastery.

The picture is a schematic, drawn with the shared robot-arm drawing library. The joint speeds are the ones needed to move the tip at 0.1 m/s along x, as in the chapter's table. Inside the singular zone the sim shows them as undefined.

Specification¶

The learning objective, evidence of mastery and content for this MicroSim are specified in Chapter 12: Kinematics: Where Is the Hand and How Do I Get There.