4 sided taper?

[Brian Penning]

Any ideas on how to make a 4 sided taper?

To add to the difficulty I need to make the small tapered pieces(plugs) to fit inside some metal tapered leg caps.
Sort of like a pyramid with a flat top.
Pyramid base is 1-3/8"
Pyramid top is 1-1/8"
Height is 1-1/2"

Really scratching my head on this one.
Thanks in advance for any and all replies.

[Charlie Plesums]

I did some pyramids as tops for columns (use either a top or stack another column, etc.). I screwed the top to a holder/jig that went against the miter fence, set at 90 degrees, but with the blade tilted away. A stop on the miter fence to determine depth of cut, and after four quick cuts and you have a pyramid with a shallow angle (anything less than 45 deg). Actually mine were octagons, so I had 8 cuts. And I put a bead around the bottom. etc.

[Chris Padilla]

http://www.sawmillcreek.org/showthread.php?t=107765

This might help you.

[Alan Mikkelsen]

There was an article in Fine Woodworking about a jig for cutting four sided tapers a year or so ago. I built it and it works pretty slick. I can cut long legs or 4" legs, with four sided tapers quite easily.

[Chris Tsutsui]

I'm not quite understanding the problem...

If you are making a four sided taper out of solid wood, then you may use a table saw taper jig. Or you can do it on a jointer. Or even on a band saw with a jig..

On the other hand, if you are making 5 panels that get put together into the shape of a pyramid with the top cut off, then do a google search for "Frustum Pyramid", because that will get you the formulas to come up with angles and lengths.

My friend helped me make a large frustum pyramid box using lock miter joints, glue, and miter spring clamps. No nails or screws.

No design software needed, just a basic frustum pyramid formula to get the volume, lengths and angles right.

http://www.flex-innovations.com/Sub%20and%20Av3_small.JPG (http://www.flex-innovations.com/Sub%20and%20Av3.JPG)

[Chris Padilla]

Chris,

Thanks for the help. If you look in the link I provided, I used SU to try and figure out something perhaps similar to what the OP was looking for. Coming up with formulas to calculate all the compound angles has escaped me so far and a search using "frustum pyramid" hasn't located anything of help. They mostly find volumes and some angles but I didn't see anything that would help a woodworking build somthing out of material that has thickness (i.e. non two dimensional) to it! Please post if you find something like this.

[Charlie Plesums]

Background... back in my engineering professor days we would gather at lunch. I posed the question that is answered below, and all the professors did calculations (at length) and came up with different answers. So I wanted a solution that didn't require calculations.

Jump forward 30 years. A few years ago Home Depot had poinsettas in small pots for only $1 apiece. So I made wood holders for the small pots, and gave each neighbor one for Christmas. You would have thought they were made of gold. The pots were easy. The pictures below are an empty pot holder right side up, and upside down so it looks like your pyramid.

Let's scale this down to your dimensions... base 1 3/8 top 1 1/8 so the base sticks out 1/8 inch farther than the top.

My technique assumes you have a sled or an accurate miter gauge on your saw, set exactly at 90 degrees, and can tilt your saw blade to exactly 45 degrees (if you want a 6 sided pyramid, tilt to 30 degrees, an 8 sided tilt to 22.5 degrees, etc.)

Since we have a 1/8 inch difference to work with, you need to make a "shim" that is 1/8 inch thick (while you are at it, make two).

Take a piece of stock that is long enough so your fingers are away from the blade. Put your shim against the miter fence and table so your stock isn't exactly flat on the table... the trailing edge of the stock is up 1/8 inch. Use your miter fence so the blade tilts away from the fence...on the left side of a right tilt blade, or vice versa. Trim the first end (for this cut, wasting as little wood as possible). If you look closely the angle isn't exactly 45 degrees, and the board is slightly longer in the part that has been raised.

Set the rip fence or other guide behind the blade, far enough out that after the next cut the long side will be 1 3/8 inches. You may have to set that guide by trial and error with scrap wood. Of course, make sure the fence or guide is back behind the blade to avoid kickback. (If your fence doesn't slide back, try attaching a board to the fence behind the blade, and use that board as your guide.


Back to the cutting... Flip the board over that you trimmed. The long side on the input side of the blade was along the rip fence, now we want the long side to be away from the fence on the output side of the blade. Cut and flip. Repeat four times for each pyramid.

The top and bottom will have a slight slope on the thickness of the wood... use the 1/8 inch shim, this time parallel to the blade, and that second 1/8 inch shim along the rip fence, to trim the top and bottom.

Post pictures of your results.