Ron Sketchpad notes/Teacup ride by transformations

Modelling the Tea-CupRide

In this activity you will use the construction and transformation facilities to model the Tea-cup fairground ride. Then explore the locus of person sitting in a cup for different platform and cup size, and different relative speeds.

Sketch and Investigate

Ron Sketchpad notes/Teacup ride by transformations

Select the line segment tool to construct two segments. /
  1. Construct line segments AB (radius/distance to centre of cup on the platform, which we will call platform radius) and CD (radius of cup)

Select point tool to create a point. Highlight (click to select) AB and Ein then in Construct menu choose Circle By Centre + Radiusto create circle centre E (platform)
Place a point F on this circle and similarly create circle centre F (cup)
First create new parameter platformangle In the Measure menu choose Calculate then New Parameter. Edit as opposite.
Highlight platformangle, right click mouse and choose Mark angle.
Double click on E to mark as Centre of Rotation
In the Transform menu choose Rotate. This will produce rotate window opposite (with marked angle selected). Click Rotate.
Double platformangle In the
Measure menu, choose Calculate.
Use the mouse to select platformangle then on the calculator keyboard “*” and “2” Click OK and mark this angle as in 3.
Highlight point person”. In the Display menu choose Trace Point.
Highlight platformangle and right click the mouse and choose animate parameter. /
  1. Construct circle centre E (platform) and circle centre F (cup).

  1. To simulate platform rotation construct point (person) on the cup and rotate cup etc. about E through some platformangle (say 30º)..



  1. The cup can also rotate about its own pivot F (or F’) We will assume that it rotates about F (F’) at twice the rate of the platform to produce the second transformed image person”


  1. We can now simulate the ride by varying the platform angle through the animation facility and tracing person”.

  1. The original cups, centre F etc.can be hidden.
Explore changing the platform and cup sizes, and relative rates of rotation. Try to visualise the locus of a person in the ride with a cup radius of half platform radius and equal rates of rotation (i.e calculated angle platformangle*2 becomes just platformangle).
How would you edit the parameters so that the cup rotates in the opposite direction to the platform?

Ron Sketchpad notes/Teacup ride by transformations