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Robot Sketcher

Math Content:

In this investigation, you can build compound arms having multiple joints of two types: one that rotates and is typical of rotating motors, and one that slides and is typical of hydraulic lifts. A circle will be used to represent a rotating joint, and a rectangle will be used to represent a sliding joint.

To simplify the problem, the device ignores any thickness of the joint and assumes that the joints can overlap with one another.

Press the Add Sliding button to add a sliding arm or the Add Rotating button to add a rotating arm. When an arm is added, the Joint Control Window will open and allow for adjustments of the length, speed, and orientation.

  • Press the Remove Arm button to remove the last arm installed.
  • To start the animation of the arms, press the Move button. The arms can be controlled, added or removed while the animation is in progress.
  • The Clear button removes the results of the animation yet leaves the arms intact. In addition, if the arms are moving, they will continue to move until the Stopbutton is pressed.

Using just these two kinds of joints, a diverse set of regions of reachable points are possible.

  1. Using just two arms (two sliding, two rotating, or one of each), what are the different regions that can be covered? Make a drawing of each region, and label important dimensions.
  2. For each region that you identified above, determine the area of the region or indicate what information you would need to know to determine the area.
  3. Build a robot with three arms. Could you cover the same region using a robot with just two arms? Explain your thinking.