Curvature [ κ ] of a curve is the degree to which it deviates from a straight line. Curvature is a property of the curve. RadiusofCurvature [ ρ ] is the reciprocal of Curvature. [ ρ = 1 /κ ] By definition, a straight line has zero curvature [and an infinite RadiusofCurvature]. By definition also, a circle has a finite curvature [and a finite RadiusofCurvature]. I find it easier to mentally translate RadiusofCurvature as the RadiusoftheCurve. The RadiusofCurvature of each point along a cam can be represented by the radius of the osculatingcircle at that point. The oscillatingcircle might be 'inside' or 'outside' the cam. 

Two Osculating Circle at two different points around the cam. One circle is outside the cam and the other is inside the cam. Think of the 'RadiusofCurvature' as the ...radius of the osculating circle. 
RadiusofCurvature  sign convention The 'sign' of the RadiusofCurvature changes when the oscillatingcircle moves one side of a curve to the other side of a curve. For example, the inside to outside of a cam. Mathematically, the sign convention of the RadiusofCurvature, is arbitrary, but should remain consistent with each analysis. However, the convention with Cams is:
Thus, with a Groove Cam, one flank is 'positive' and the other flank is 'negative' RadiusofCurvature. Note: it is possible to have a 'negative' radius for the CamFollower! The CamFollower is a 'housing' that surrounds the cam. RadiusofCurvature ( ρ ) = 1/ Curvature ( κ ) 

Radius of Curvature Convention for Planar Cams 

Usually, you must make sure the:  Cam RadiusofCurvature  > CamFollower Radius. It is useful to consider the ratio of the Cam Radius against the CamFollower Radius.
RadiusofCurvature  RuleofThumb
In MechDesigner, we use the CamData FB to plot the Radiusof Curvature of Cam1 and Cam2. In this graph, the green identifies the radius of the camroller. The graph shows that the camprofile has both positive and negative radiiofcurvatures. Note: when the radius changes from '+ve' to '–ve', or vice versa. it passes an inflectionpoint. This is when the cam is flat and the radiusofcurvature is infinite [∞]. The graph shows a vertical line when the radiusofcurvature changes from +∞ to –∞, or vice versa. 
If the RadiusofCurvature of the cam is small, then you must make these design checks: Contact Hertzian Stress : As the RadiusofCurvature gets smaller, then for a given Load, the ContactStress between the cam and the camfollower becomes larger. Heat Treatment : Heat treatment is more likely to crack the steel if its RadiusofCurvature is small. FlatFaced Followers : When the camfollower is a FlatFaced Follower, the RadiusofCurvature of the cam must be +ve at all times. 

Undercutting Note: in MechDesigner, the camfollower always moves with the motion as kinematically specified. In your machine, the camfollower's motion becomes controlled only by its contact with the cam, of course. Thus, if the cam profile is undercut, the camfollower cannot move with the motion as kinematically specified. In MechDesigner, you can scrutinize the model to look for a 'dovetail'  see model to the left. However, the best way is to use the CamData FB and a Graph FB. In the Graph, make sure the you plot the correct RadiusofCurvature! Use the Yaxis dropdown in the open graph to select 'RadiusofCurvature 1', or 'RadiusofCurvature 2', for Cam 1 or Cam 2 respectively. The number of the Cam is at the contactpoint in the graphicarea. 

Interference
 Cam's RadiusofCurvature  > Roller Radius 

Video of Undercutting  Video is very Slow! The RadiusofCurvature is less than the radius of the camroller.
However, the CamFollower cannot actually not follow the specified motion as the camfollower has nothing to follow! Too much metal has been removed from the cam.

Schematic of Maximum Contact Stress of Cylindrical and Barrel CamFollowers 
Whether to use a CylindricalCamFollower or a Barrel CamFollower is a function of the type of machine and how well the follower and cam's rotationalaxes can be aligned. Cylindrical Roller  missalignment When the rotational axis of a cylindricalroller is not parallel to the rotationalaxis of a cam, the camfollower will tilt relative the cam's surface, and roll along its edge.  see the bottom and left example in the image to the left. The contact is distorted. The maximum value of ContactStress is significantly greater than the nominal value that is calculated for 'linecontact'. Barrel Rollers. If the rotationalaxis of the camroller is not parallel to that of the cam, the camfollower will tilt relative to the cam's surface. In this case, the contact moves across the cam surface, but when the tiltangle is within limits, it does not roll along its edge. The contact is not distorted much. The maximum value of ContactStress is not more than the nominal value that is calculated for 'ellipticalcontact'. The nominal maximum contactstress of a barrelroller is greater than that of a cylindricalroller. However, when a camfollower tilts the actual maximum contactstress of a cylindricalroller is much greater than that of a crownroller. The permissible tilt angle of a cylindricalroller is very small, ( <0.1° ), and thus a barrelroller is a good design option in many cases. 

Radius of Curvature Convention for Cam and Barrel Rollers 
