In the geometry analysis, the camming angle of the Black Diamond #3 Camalot was determined to be 14.9653 degrees. To verify this measurement, the cam angle was measured directly by placing the cam in a vice with parallel plates lined with white paper. The cam was inked so that when it was placed in the vice, it would mark the contact point of the cam with the walls of the vice. The distance of the two plates were set at various widths and the cam angle was measured at each width. The measurements and results are shown below.
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axle separation = 0.961833 in. |
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Outer Lobe |
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crack width (in) |
parallel dist from axle to contact point (in) |
perp. dist from axle to contact point (in) |
hypotenuse (in) |
cam angle (deg) |
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2.231 |
0.4475 |
1.596417 |
1.657951 |
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15.659 |
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2.5 |
0.445 |
1.730917 |
1.787204 |
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14.41789 |
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2.66 |
0.472 |
1.810917 |
1.871417 |
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14.60864 |
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2.883 |
0.5275 |
1.922417 |
1.993475 |
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15.34398 |
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3.16 |
0.547 |
2.060917 |
2.132273 |
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14.86449 |
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2.2155 |
0.441 |
1.588667 |
1.64874 |
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15.51419 |
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2.4125 |
0.49 |
1.687167 |
1.756881 |
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16.19476 |
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2.6425 |
0.3845 |
1.802167 |
1.842728 |
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12.04372 |
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2.6425 |
0.533 |
1.802167 |
1.879333 |
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16.47585 |
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3.016 |
0.3995 |
1.988917 |
2.028642 |
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11.35748 |
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avg |
14.648 |
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Inner Lobe |
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crack width (in) |
parallel dist from axle to contact (in) |
perp. dist from axle to contact (in) |
hypotenuse (in) |
cam angle (deg) |
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2.231 |
0.349 |
1.596417 |
1.63412 |
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12.33168 |
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2.5 |
0.426 |
1.730917 |
1.782568 |
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13.82641 |
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2.66 |
0.484 |
1.810917 |
1.87448 |
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14.96358 |
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2.883 |
0.42 |
1.922417 |
1.967762 |
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12.32405 |
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3.16 |
0.55 |
2.060917 |
2.133044 |
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14.94238 |
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2.2155 |
0.359 |
1.588667 |
1.628724 |
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12.73358 |
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2.4125 |
0.4505 |
1.687167 |
1.746276 |
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14.95009 |
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2.6425 |
0.413 |
1.802167 |
1.848884 |
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12.90751 |
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3.016 |
0.4955 |
1.988917 |
2.04971 |
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13.98935 |
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avg |
13.66318 |
As can be seen from above, these measurements have a large amount of scatter, with the first and second sets of the calculated cam angle having standard deviations of 1.69 and 1.12 respectively. This may have been due to the fact that the surface of the cam lobe is notched. Whereas a point in the area where the notch is located would normally be the contact surface, the contact point is actually a point to the left or right of the notch as the notch itself is not able to make contact with the surface. This leads to a few degrees of error; however, when these values are averaged, this error is somewhat reduced.
When measured directly, the outer and inner cam lobes were found to have cam angles of 14.648 and 13.663 degrees respectively. These values are reasonably close to the value of 14.9653 degrees determined from geometric analysis of the cam lobe shape. |