CAD-based sketching 'can be applied to virtually any problem'

CAD software often includes motion analysis, which uses multibody dynamics to simulate mechanisms.

This can provide information on motion paths, velocities, accelerations and reaction forces within mechanisms. 

Although these tools can be very useful, they do not provide much assistance with actually designing the mechanism in the first place. They assume a design exists and allow its performance to be tested. The constraint-based sketcher central to any parametric CAD software can be used as a powerful mechanism synthesis solver.

Mechanism synthesis involves determining the joint positions and linkage lengths required to produce some desired movement. This may be specified in many ways, but conventionally synthesis is classified into three types of problem: 1) Motion generation moves a line through a number of prescribed positions; 2) Path generation moves a single point through a prescribed path; and 3) Function generation attempts to map an input function to an output function – this often involves a changing velocity ratio between an input link and an output link.

A new approach

Mathematical methods involve forming kinematic equations for each link in a mechanism and constraining these to share common joint positions and any other requirements to satisfy the specified movement requirements. The linkage lengths are unknowns in these equations and mechanism synthesis then becomes the solution of a set of simultaneous equations. This approach can be technically challenging and not intuitive.

The sketcher in parametric CAD software uses geometric constraint solving to determine unknown geometry parameters given a very versatile set of constraints. These may be non-parametric, ie tangent, horizontal or coaxial, or parametric, ie a distance, angle or radius. The solver will find the positions of geometric elements that satisfy the given constraints. 

Repurposing CAD

This is an ideal tool for the synthesis of mechanisms. It enables virtually any synthesis problem to be defined, in 2D or 3D space, and to be solved in a similar way to the conventional mathematical approach to mechanism synthesis. However, it does this through an intuitive graphical interface.

Graphical synthesis of a four-bar linkage to generate a motion involves finding joint positions using methods such as constructing perpendicular bisectors. This is quite intuitive when you know how, but different methods must be learned for each class of problem. Using CAD the basic method is always the same, making this approach even more intuitive. With a little imagination it can be applied to virtually any problem, even complex 3D mechanisms. 

Constraints can be defined to generate paths, motions or velocity functions. Constraints can also be used to limit transmission angles or linkage lengths, providing a sophisticated mechanism design methodology. CAD-based sketching combines the intuitiveness of graphical methods with the accuracy and versatility of mathematical methods. And it does all this using the tools designers are already familiar with.