Mechatronics in Design: Exact-constrain design offers repeatable position, easy assembly, robustness

Keep complexity intrinsic, keep functions independent, improve designs with self-help, plan load paths in assemblies. These are some of the guiding principles that expert machine designers have gleaned from years of practice. Sadly, these are not well-publicized, and are even often overlooked in machine and machine elements courses that most new engineers have most likely taken. One other guiding principle, perhaps more important than the ones mentioned, is exact-constraint design. (References 1 and 2 provide material on that topic, with Reference 2 serving as the source for much of this column.)

Precision machines are essential elements of an industrial society. A precision machine is an integrated system that relies on the attributes of one component to augment the weaknesses of another. Characteristic to all precision systems is the high level of determinacy they require. Predictable and reproducible behavior is a key quality that only carefully designed, robust mechanics and control systems can achieve. To achieve excellent and predictable behavior, the mechanisms require, among other things, exact constraint—just enough constraint to define a position or motion. Unlike overconstrained designs, exactly constrained designs boast a repeatable position, easy assembly, and robustness to wear and environment. They have no binding, no play, no internal stress, and no loose-tolerance parts.

A 3D object has six degrees of freedom—the number of independent coordinates necessary to describe a system’s motion—three translations and three rotations. Selectively constrain these degrees of freedom to obtain the desired motion or structure. If you rigidly constrain a component at more places than necessary—by, for example, placing three bearings on one shaft—these places will “fight” with each other.

The design of high-quality precision machines depends primarily on an engineer’s ability to predict how the machine will perform before he builds it. The most important factors affecting the quality of a machine are its accuracy, its precision or repeatability, and the resolution of its components and the manner in which they are combined. Accuracy is the ability to tell the truth, precision is the ability to tell the same story over and over again, and resolution is how much detail the story has. Designing a machine that has good accuracy, precision, and resolution is not a black art.

Consider the use of linear drives for scanning. They often comprise a motor attached to a lead screw, which in turn drives the scanning carriage. A first design shows a cyclic error in linear motion (Figure 1a). Trying more accurate machining, better part alignment, and a more expensive lead screw yields no success. A constraint analysis shows that the design is overconstrained. The motor attaches rigidly to the lead screw, so the motor requires only one constraint: to prevent the rotation of its housing. The compound flexure eliminates the problem by eliminating the need for an expensive lead screw, accurate machining, and assembly steps (Figure 1b).

Understanding how to transform basic physical principles into working concepts with predictable behavior is the key to achieving high accuracy, high speed, and high reliability.

About the Author
Kevin C Craig, PhD, is the Robert C Greenheck chairman in engineering design and a professor of mechanical engineering at Marquette University’s College of Engineering.

References:
1. Blanding, Douglass L, Exact Constraint: Machine Design using Kinematic Principles, ASME Press, 1999.
2. Skakoon, James G, The Elements of Mechanical Design, ASME Press, 2008, ISBN: 978-0-7918-0267-0.