Suggested Technique for Dimensioning Radius of Curvature of a Spline

There are many occasions when a spline curve is sketched for a datum curve that can then be used for various features, such as trajectories for sweeps and boundary curves for a surface created from boundaries. In the first case, the spline's basic shape and internal point locations are the only concern, but when working with surfaces, the conditions at the endpoints of the curves are critical for determining tangency conditions to other surfaces. This is where radius of curvature of the endpoint of a spline curve has great importance. Simply defining tangency for the endpoint is not enough to control the topology of the resulting surface. This technique will explain how the radius of curvature is dimensioned and will show how the values can directly affect the features created from the curves.

Procedure
  1. Start with a default coordinate system and default datum planes, renamed to FRONT, TOP, and SIDE for clarity. See Figure 1.

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    Figure 1

  2. Select Feature, Create, Datum, Curve, Sketch, Done, and select FRONT as the sketching plane and TOP as the Top reference plane. Sketch the section shown in Figure 2 using Sketch, Adv Geometry, Spline, and select Both from the TANGENCY menu to allow for angular tangency dimensions of the spline endpoints. Dimension and Align the spline endpoints to TOP and SIDE, and then dimension the angular tangency at each endpoint. This is accomplished by selecting the spline 2 times with the left mouse button, the endpoint 1 time with the left mouse button, the datum plane reference 1 time with the left mouse button, and then place the dimension with the middle mouse button. For the radius of curvature dimension(sd0), select the endpoint of the spline with the left mouse button and place the dimension with the middle mouse button. Regenerate the section and select Done to complete the feature.

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    Figure 2

  3. Now create datum points PNT0 and PNT1 by selecting Feature, Create, Datum, Point, On Curve, Length Ratio. Select the curve, and enter a value from 0 to 1 for the ratio of placement along the curve-in this case, enter 0 and 1 for the value for each point. See Figure 3.

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    Figure 3

  4. Now, to create the remaining datum curves to be used to bound the surface, select Feature, Copy, Move, Independant, Done, select the curve and the points, select Done, and then select Translate from the MOVE FEATURE menu. Select the FRONT plane for the direction that the move will be perpendicular to, and Flip the direction and enter an offset value. See Figure 4. Then perform the same steps, only select Mirror instead of Move from the COPY FEATURE menu, and select the SIDE plane to mirror about. See Figure 5. For the curves to close the loops, create Datum, Curve, Thru Points, Done, select Define from the Datum Curve: Through Points Dialog Box, select Single Point, select PNT1 and PNT3, Done, and OK from the Dialog Box to complete the feature. Repeat these steps to create the curve through PNT4 and PNT6, and then PNT5 and PNT7.

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    Figure 4

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    Figure 5

  5. Now create 2 surfaces from boundaries for the left and right side areas. For more information on how to create a Surface from Boundaries, please refer to Suggested Technique for Creating a Surface From Boundaries. The results should look like Figure 6.

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    Figure 6

  6. The surfaces appear to have a smooth, tangent intersection because the angular tangency dimensions set the endpoints to join at 90 degrees when shaded using View, Cosmetic, Shade, Display. See Figure 6 above. In most situations, this is acceptable, but not when working with many surfaces joined together, as in a body panel for an automobile. The values of the radii of curvature could be different, if dimensioned at all. This will cause a "seam line" to be seen in the panel, which is unacceptable in most cases. This will not be viewable in the current model necessarily, but could be seen in the final production component. To show the differences more easily, Modify the radius of curvature values for each of the 4 curves to the values shown in Figure 7.

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    Figure 7

  7. The surface will still be smooth over the transition, due to the angular tangency, but select Info, Crv Analysis, CrvtureDisp, Query Select and select the 4 curves underlining the surfaces. The scale may need to be changed in the CRV DISPLAY menu, but the effect is the same. With different radius values, the differences can be seen in the curves, which will directly translate into the surfaces created from those curves. Select Info, Srf Analysis, Porcupine, and select each surface. Change the Scale 1st if necessary. See Figure 8 for the curve analysis, and Figure 9 for the surface analysis.

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    Figure 8

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    Figure 9

  8. Now Modify the values for the radii of curvature to 50 for each and perform the Crv Analysis and Srf Analysis again to see how the curves and surfaces are corrected. See Figures 10 and 11 respectively for the results.

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    Figure 10

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    Figure 11

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