A Larger Example

To practice using the constraint solver for a more significant problem, you should construct the following profile:


 
    Goal object

The base should have a horizontal axis, and the two handles should be able to be rotated to new positions by changing one dimension related to each handle.

Goal Configuration Hints

If you don't know where to begin, the diagrams below show the configuration with the auxiliary entities and with the dimensioned constraints in place.

 
Auxiliary Geometries

 
Dimensioned Constraints

As a further hint, consider building the mechanism up gradually, verifying the correctness of the constraints at multiple stages of the construction.

Our Solution

Here we give a step-by-step construction of the configuration.

Step 1

Begin with an auxiliary axis.

Place two points Pt3 and Pt4, one near the origin of the axes, the other along the positive x-axis.

Invoke the On constraint, and make Pt3 lie on the x-axis and the y-axis, and Pt4 lie on the x-axis.


      Step 1

Step 2

Place two arcs around the points.

Place two segments between the arcs, establishing on constraints between the end points of the arcs and the segments in the process.


      Step 2

Step 3

Make Ar7 concentric with Pt3, and Ar10 concentric with Pt4.

Make Sg12 tangent to Ar7 and Ar10.

Make Sg14 tangent to Ar7 and Ar10.

Establish radii for Ar7 and Ar10.

Establish an angle constraint between Sg12 and Sg14.


      Step 3

Step 4

Regenerate.


      Step 4

Step 5

Modify the values of the constraints so the radius of Ar7 is 50, the radius of Ar10 is 100, and the angle is 20.

Regenerate.


      Step 5

Step 6

Input a circle concentric with Pt3.

Input a circle concentric with Pt4.

Set the radii of the circles to be 25 and 40, respectively.

Regenerate.


      Step 6

The base of the object is now completed.

Step 7

(This step establishes the auxiliary lines needed to construct the two handles.)

Add three auxiliary lines. One of these should go approximately through Pt3, and the other two through Pt4.

Establish an on constraint between Pt3 and the line through Pt3, and between the other two lines and Pt4.

Make the two lines through Pt4 perpendicular.

Establish an angle constraint between the line through Pt3 and the y-axis.

Establish an angle constraint between either line through Pt4 and the x-axis.

Regenerate.


      Step 7

Step 8

(This step adds the handle on the right side of the figure.)

Construct an arc whose end points lie on one of the lines through Pt4.

Make this new arc concentric with Pt4.

Input three segments, connecting them to the end points of the arc.

Make the two segments adjacent to the arc be tangent to the arc.

Make the end segment perpendicular to one of the other two segments.

Establish a distance constraint between two points delimiting one of the long edges of the handle.

Regenerate.


      Step 8

Step 9

Establish the radius of the arc constructed in the previous step, and set its value to be 45.

Modify the distance constraint of the previous step so the length of the handle is 300 units.

Regenerate.


      Step 9

Step 10

(This step constructs the handle on the left side.)

Input four segments as an approximate rectangle, so that the auxiliary line containing Pt3 is an axis of the rectangle lengthwise, and so that the width of the rectangle is approximately the diameter of the circle on the left of the base.

Establish on constraints between the two end points of the edge running through the circle on the left of the base and the circle itself.

Establish perpendicularity between any three pairs of the four segments.

Establish that one long edge of the rectangle is parallel to the auxiliary line containing Pt3.

Establish that one long edge of the rectangle is tangent to the circle on the left of the base.

Establish a distance for one of the long edges of the rectangle.

Regenerate.


      Step 10

The mechanism is now complete. The handles can be moved by adjusting the angles between the axes of the handles and the axes of the plane.