SEED Unit Design - Cam Mechanisms < >

Provided the number of independent dimensions specifying the mechanism is restricted to those defining a translating follower the synthesis to find the minimum cam size compatible with the kinematic constraints can be completed readily using a spreadsheet. Headings of the example forming the basis of Figures 17 to 24 are shown in Figure 16. They define a disc cam driving a radial translating follower, i.e. with zero offset. The basic dimensions specifying the segment angle (1000) and lift (25mm) are entered in cells E7 and E8 respectively The non-dimensional forms of the follower displacement, velocity and acceleration, equations (7) to (9), are computed in columns B, C and D respectively at 0.02 increments of the normalised cam angle (column A). Only the first 2 rows have been included in Figure 16. Thus part of the program is common to all cam mechanisms having this configuration and cycloidal motion. Hence the dimensions of a specific mechanism are obtained quickly and the significance of changing a dimension is readily apparent. Allied with the graphics facility relating the critical parameters, the User can optimize the design, for example to find the least prime circle radius compatible with a given maximum pressure angle.

Figure 15a Ill-proportioned cam having undercut convex profile

Figure 15b Enlarged view of undercut convex cam profile

Figure 16 Spreadsheet Layout for computing Pressure Angle data. (Use of dimensionless parameters for the intermediate calculations enables the results for different cam angles to be obtained by entering the new value in one cell.

These data form the basis of Figures 17 to 24)

At this stage of the kinematic design it is vital to check for profile undercutting by extending the spreadsheet to derive the data for drawing the graph of profile radius vs cam angle. The smallest radius must meet this criterion whereas infinite radii pose no problems so this relationship can be shown sensibly by using the logic.

Profile Co-ordinates

The profile has to be generated indirectly from the locus of the roller centre as the envelope of the roller circumference. This curve is a complex function specified by calculating the coordinates at small increments of cam rotation. These points are then interpolated to determine the cutter path of the machine-tool. For the general case of a disc cam driving an offset translating follower the cartesian co-ordinates of the cam profile are:

Drawing the profile shape is an effective check. This can be done with the spreadsheet by calculating these co-ordinates and drawing a scattergraph, Figure 19. When constructing this graph care must be taken to equate the scales of the x- and y- axes. Figure 18 Undercutting test: limiting maximum radius of curvature