SEED Guides Tutor's Guide - Cam Mechanisms < >
11. The Spreadsheet10.1 At this stage the requirements for the spreadsheet analysis should be appreciated. The original work was done on a Macintosh Apple SE using MSc Excel v4.0. Fig 16 of 'Cam Mechanisms - Unit Design' guide shows the top 21 rows of the worksheet used to obtain many of the charts used to illustrate 'Cam Mechanisms - Unit Design' guide .
10.2 A copy of this worksheet suitable for the Apple Macintosh or the PC version of MS® Excel can be downloaded from the SEED website. http://www.cad.strath.ac.uk/~bill/seed.htm. The worksheet utilises a cycloidal cam law.
10.5 The principles of using non-dimensional parameters to define the follower motion are explained in the Cam Mechanisms - Unit Design¹ guide , pages 9 and 10; equations (2) to (9). The normalised cam angle u for one motion segment is entered at increments of 0.02 in column A; the normalised follower displacement w [for cycloidal motion] calculated in column B from equation (12) and the non-dimensional [not normalised, see Appendix E] follower velocity and acceleration from successive derivatives of equation (12) in columns C and D respectively. These do not require modification once entered or computed from an earlier entry. Corresponding data for other cam laws can also be entered at the expense of expanding the worksheet.
Charts are obtained readily, see 'Cam Mechanisms - Unit Design' guide , page 11, Figures 11 to 13.
10.6 The same principles are used to calculate the non-dimensional solution for the pressure angle using equation (T14) above for the range, say, 0.8 ¾ (Ra/H) ¾ 3 in columns H to M and then calculating the actual value of a by evaluating the arctangent and converting from radians to degrees. A further column, set at the constant value of the maximum permitted pressure angle, must be added to superimpose the limiting value on the chart. Again these values are modified just by re-entering the new value of the controlling dimension or ratio in the appropriate cell.
10.7 The same approach is used to find the radius of profile curvature; this always has to be found for a specific segment angle.
10.8 Deriving the data for blended motions is more complex: the spreadsheet analysis outlined above must be adapted since blending involves the combination of two motions having different "notional" segment angles and lifts beginning at different points on the chart. Smooth transition between the motions is achieved by joining the displacement curves at the point of maximum follower velocity [i.e., zero acceleration] and equating these velocities; see 'Cam Mechanisms - Unit Design' guide , Appendix A and Figures 20 and 21.
The spreadsheet package used by the author required a complete set of values in every column. Hence zeros had to be entered at both ends of the displacement curve of the "notional" inner portion, causing the two [almost] vertical lines AB and CD in Figure 20. These have no significance and disappear if the chart shows only the resultant motion. [Similarly, zeros have to be added to the data defining the velocity and acceleration of the inner portion, but these do not affect the chart as the resultant lines coincide with the cam angle axis throughout.]
When applying this principle to student assignments it is recommended that the analysis be simplified by restricting the assignments to those cam laws [i.e., most, but not all] which attain maximum follower velocity at mid-stroke, such as those defined by equations (10) to (13) of the 'Cam Mechanisms - Unit Design' guide
