basic geometry of linkages explained to caveman

[thomas harris]

I am trying to design a simple peck drilling rig for my small lathe. It has been some time since geometry or trig, so things are rusted solid up there. Is there a tutorial online or elsewhere which will provide the basic principles of moving a piston forward with a lever system explained. I am having difficulties understanding the nonbinding linear motion and the linkages required to achieve this. I can simply grab some flat stock and start experimenting with different legnths and such, but this seems like a bad idea. what i am after is something that covers this with text and animations if possible.

[hammermill]

here is a simole aproach

http://video.okayclip.com/?w=bh4L65V1Sq ... -the-lathe

[thomas harris]

that shows the parts, and shows it does work, but it doesn't dwell on the way the parts interact to achieve the movement.

[SteveM]

On that setup, the fact that the shaft connects to the handle with a slot allows the freedom of movement to keep it from binding.

Other setups use a link that has two pivots to take up the movement that would cause binding.

Take a look at a lever collet closer. The handle mounts to a link and the link mounts to the headstock. If the handle mounted to the headstock, it would bind.

Here's a tailstock drill with such a setup.


Here's another:


The extra link provides the "slop" needed to eliminate the arc motion of the handle.

Steve

[thomas harris]

i think i see some daylight on this now. basically more distance between those links means more distance of travel in a straight line, but this changes very little with small distances between the links. so should i intentionally put some extra slop in the pins to allow maximum lateral movement?

[stevec]

I don't think "slop in the pins" is the way to go. two pivot points for the fulcrum linkage or maybe a slot in the hand lever will eliminate binding but extra play anywhere in the linkage isn't advisable.

[SteveM]

Steve has it right. The "slop" for which you are looking is provided by the motion of the link, not by any slop in the pivots.

Make yourself a cardboard model with push pins for pivots stick into a piece of wood and you will see the action.

Steve

[hammermill]

a wooden model is a great way to wrap the ole brain around something

[thomas harris]

i suddenly feel small and insignificant, yet relish the idea of grasping something a bit better than before. I may try a model of some kind. I was trying to draw them as simple triangles with changing legs length as the pivot moves, but got very confused. geometry and trig were about 30+ years ago. i tend to overanalyze, but that will likely not change.

[dly31]

As you know, a triangle is rigidly defined by the length of the 3 sides. In order to make the linkage moveable you have to either add a 4th side or provide a slot or other means of allowing the length of one side to change.

I think the rate of change of a side with a varying angle would be the 1st derivative of a sine or cosine function but I am not nearly smart enough to make any use of that bit of information!

[thomas harris]

ouch! that last part give me a headache.

[dly31]

Me too!

In case you can't tell, the little link added to the levers has to be free to pivot slightly at both ends for it to work.

ouch! that last part give me a headache.