An Application of Geometric Constraint Solving

One application for geometric constraint solving is in the area of Computer Aided Engineering, particularly in the branch of mechanical engineering design. A method for designing an object with the computer should be strongly visual in order to provide an intuitive interface, but must also provide a way to produce a careful, detailed description. One approach for reaching these two disparate goals is to apply geometric constraint solving to the problem of geometric data input. Through a graphical user interface, the user can sketch a rough outline of the object to be constructed. By adding constraints such as the length of an edge of the object or the angle between two edges, a precise description of the object is obtained. Such a system has been designed and implemented with points, lines, and circular arcs in the plane as allowable geometric entities, and constraints such as an angle between entities, distance from one entity to another, incidence, and tangency (in the case of circular arcs)[7]. The object obtained as the solution to the constraint problem can then be swept or rotated to obtain a three-dimensional object. Additional features can be added by sketching on a two-dimensional plane of the resulting object, and extruding the sketched region, or cutting a slot or hole in that shape through the object. As a specific example, we show how a control arm is constructed and modified in a feature based design system currently under development by Chen[17] The system interfaces with the two-dimensional constraint solver of Fudos [33] for its geometric input.

Construction Step 1

A sketch is drawn and properly dimensioned and constrained. Not displayed are tangency constraints between the arcs and the adjacent line segments.

Construction Step 2

The two-dimensional sketch is extruded to obtain a three-dimensional object.

Construction Step 3

Another sketch is drawn on an interactively chosen plane and is properly dimensioned and constrained. An additional constraint not shown in the diagram is that the two arcs on the right are concentric.

Construction Step 4

This new feature is then extruded from the face on which it was sketched.

Construction Step 5

A hole is cut from the top face of the previous geometry.

Construction Step 6

A slot in the side planar face is depressed.

Construction Step 7

A keyway is cut from the top face.

Construction Step 8

A hole is cut from the left side. This is the final design.

Shaded image of control arm

Modification of control arm

A modification is made in the second feature so that the angle changes from 30 degree to 60 degree. This change is automatically generated from the modified Erep program.