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Transform Chain Calculator

Run the Transform Chain Calculator MicroSim Fullscreen

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Description

Turn the two joints of a flat two-link arm and watch the two link vectors add up to the position of the tip. Then work out one coordinate of the tip in six problems, using the forward kinematics formulas, and check each answer. Used in Chapter 12.

The arm has two links of 0.10 m. The tip is at

  • x = l1 cos(theta1) + l2 cos(theta1 + theta2)
  • z = l1 sin(theta1) + l2 sin(theta1 + theta2)

with x forward and z up. An answer counts as correct when it is within 0.001 m of the right value.

Lesson Plan

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

  1. Explore. Move the theta1 slider and then the theta2 slider. Which one turns the whole arm, and which one turns only the second link?
  2. Read the triangles. Each dashed triangle shows how far forward and how far up one link goes. Add the two forward sides to get x, and the two upward sides to get z.
  3. Six problems. Choose Six problems in the menu. Work each one out on paper or with a calculator, type the number in metres, and press Check. You get one attempt at each, and 5 of 6 is mastery.
  4. Think about it. A calculator set to degrees takes 30 directly. Python's np.sin and np.cos take radians, so a program must convert the angle first with np.radians.

The picture is a schematic, drawn with the shared robot-arm drawing library. An angle of 0 degrees points forward, positive angles turn counter-clockwise, and theta2 is measured from the line of the first link.

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.