Tick Talk on EsoxRepublic.com

There’s a yawner of a title for ya! Probably of little interest to most. I would wager that there are more who should be interested, if they knew what was good for them. Especially GearTrax users.

Curvature of a spline is the inverse of the radius of the spline at a given point. A curvature of zero equals infinite radius = straight. Certain geometry is sensitive to curvature. Curvature continuity is important for airfoils and cams. Involute curves used to define gear teeth are also curvature-sensitive.

Curvature of SolidWorks Splines

One tool for evaluating the curvature of a spline is the curvature comb. The curvature comb shows a relative indication of a spline’s curvature. Where the comb’s “teeth” are long, the curvature is high. The comb tooth length decreases as curvature approaches zero. Inflection points are indicated where the comb switches sides.

An important phenomenon of SolidWorks splines is that they have zero curvature at their endpoints when they are initially created. The curvature will stay zero until the spline endpoints are altered somehow. Spline endpoints could be altered by moving, trimming, adding constrains, or manipulating control handles.

Spline with curvature comb. When open splines are first drawn in SolidWorks, they have zero curvature at their endpoints.

Involutes and Curvature

One case where curvature is important is when drawing an involute. An involute is the curve needed for gear teeth. It is graphically derived by unwrapping a string from a circle. There is also a mathematical formula.

One common method of drawing an involute is to draw a spline through a series of points, derived either mathematically or graphically. However, if one were to simply draw a spline through a set of points and walk away without further editing, that spline would have noticeable error. The endpoints of the spline would be straight (zero curvature).

At no point in an involute is there zero curvature! In fact, an involute has infinite curvature at its root. Forcing a spline to zero curvature at the involute root would immediately introduce error to the rest of the spline as it interpolates its path between defining point. The spline would wander inside and outside of the ideal involute path as it attempts to meet all of the defining points after starting with zero curvature. Additional error is also introduced by the zero-curvature end condition.

…and GearTrax

After all these years, I finally took a look at GearTrax. This after seeing a post about gear design and having a moment of idleness and curiosity.

Of course, I downloaded some samples. I set about inspect the gear profile curvature. I was curious to see how the models were constructed, and what the involute looked like. I honestly expected that GearTrax would have dealt with this issue somehow. However…

to be continued…