Kinematics in Fixturing Design
Kinematics is the geometry of motion. Engineers use kinematics every day in machine design when considering the various motions necessary to move an object or part from point A to point B with accuracy and repeatability. It especially comes into consideration when locating and/or aligning parts within an automated system. It’s pretty common to need to accurately align one part relative to another in order to perform an assembly or inspection task, and engineers wrestle with the best way to accomplish that in their designs. To get accurate alignment, you need to consider constraints.
Every object in space has six degrees of freedom. By constraining one or more of those degrees of freedom you restrict and control the movement of that object. To precisely hold an object, you need to constrain all six degrees of freedom – never more, never less. This is known as a kinematic constraint. Under-constraint leads to free motion, and over-constraint leads to indeterminate location, both of which introduce uncertainty that will have a negative effect on accuracy. It is important to note that many kinematic couplings are not designed to restrict all six degrees of freedom. Often, kinematic principles are used to define linear or rotary motion by leaving one or more of degrees of freedom unconstrained.
What are the methods used to constrain all six degrees of freedom? There are several fixturing methods that add up to six degrees of constraint. Consider the three ways to constrain a sphere:
Ball on flat. Constrained in one direction.
|Ball in vee-groove. Constrained in two directions (two points of contact)|
|Ball in cone. Constrained in three directions.|
Knowing this, you can select fixturing design methods that add up to six degrees of constraint in order to precisely hold a part or object. If your fixturing uses all three methods shown above, you would constrain all six degrees (1 on flat + 2 in vee + 3 in cone = 6) and the manufacturing tolerances could be in the millimeter range with positioning repeatability in the micron range. It might look like this:
Another fixturing design option would be a Kelvin kinematic coupling, which also constrains all six degrees of freedom, but does so by using three balls in three vee grooves. It would look something like this:
A third fixturing design choice would be a kinematic coupling which uses combinations of spheres and cylinders. This approach can be very economical to produce. It constrains all six degrees of freedom (2 contact points x 3 = 6) and would look like this:
There are a couple of considerations to keep in mind when selecting the design of a kinematic coupling: accuracy and load carrying capacity. As the load goes up, the flexing of the very narrow contact surfaces of small spheres and cylinders or vee-grooves will cause fretting, which is a wearing of the contact surfaces caused by friction. Case in point: our engineers were faced with the requirement to accurately hold components with 1000 pound force. In that scenario they used a canoe sphere, which mated to a vee-block, and are designed for higher load capacity by altering the shape of the sphere. It looked like this:
A pinned joint connection might have been considered due to their high load capacity, but they have poor repeatability even with tight tolerances and they always have slop, which adds to the expense. So in this case a kinematic solution was necessary. In the common situation where alignment accuracy is the primary concern, our engineers designed a part nest using kinematic principles, as shown below.
This design uses three vacuum cups with center posts for establishing elevation and each constrains in one direction (flat). It also has three fixed “fingers”, or flat points. Two additional, flexible fingers are used to help “snug” the part into the nest. This is not considered over-constraining due to their flexible, spring-loaded nature. This type of design is considered to be planar kinematic and is highly repeatable.
In conclusion, whichever way you design your fixturing, if high precision and accuracy are required then a kinematic coupling which constrains all six degrees of freedom – never more, never less - is the best option.