Slider Crank Mechanism Variations

An offset slider crank is used where the normal in line cannot be used due to obstructions etc. No slider crank that I am aware of produces pure sinusoidal motion.

There is however a cycloid gear of 1/2 the pitch diameter of an internal ring gear that produces true sinusoidal motion. (2/3 way down page, click on image.)

<http://stirlingsouth.com/animations/gear.gif>

Straight Line Sinusoidal Motion Mechanism

Its been many years since I've been involved with this, but if I'm not mistaken, a Scotch Yoke in a rotating disk will produce sinusoidal motion if the pin or shaft in the center of the Scotch Yoke square is allowed to move only in the reciprocating direction.

I did not have the time now to look up internet references, but a Scotch Yoke is just a square bearing block which moves back and forth in a slot in a rotating disk or gear. The slot must be on center in the disk, so the disk or gear will need to have an overhung or cantilivered support shaft bearing, with the slot in the free face of the disk or gear. Opposite surfaces of the square form the bearing surface which mates with the walls of the slot. A hole in the center of the square forms the bearing surface for a shaft, which as stated, is allowed to move in the direction of reciprocation only. So if the reciprocation direction is vertical, the bearing block rotates as the disk does, but moves only vertially regarding translational motion. Thus, motion in the direction of reciprocating motion is sinusoidal.

Bernie Katz

Stayed up a bit later to look at one internet reference:

http://www.brockeng.com/mechanism/ScotchYoke.htm

Customarily a square bearing block is used between the pin and slot to provide bearing surface to control pin wear. That is not shown in the link illustration, although the principle shown is correct.

Bernie Katz

berniek: You are correct. The Scotch Yoke does produce true sinusoidal motion at the expense of increased friction and varying forces in the components.

IMHO the cycloid gear solution is a most elegant way to obtain truly sinusoidal motion from a reciprocating slider or piston to a rotating shaft or vice versa.

dkamesh11,

I'm not sure what you mean by forward and return stroke ratios, since the forward and return strokes are of equal displacement.

All other things being equal, changes in the offset effect the total displacement, and the velocity, acceleration, and mechanical advantage profiles of the strokes. The actual changes depend on the relative values of the crank radius, connecting rod length and offset.

Offsets were employed on many machines, including some engines, and the presence and/or amount of offset is part of the design process for employing a slider crank mechanism to a particular application.

One link that shows a slider crank diagram with an offset and some formulas:

http://www.mathcad.com/library/LibraryContent/MathML/couplercurve.htm

Greg

I'm not sure what you mean by forward and return stroke ratios, since the forward and return strokes are of equal displacement.

But they do not necessarily require the same time to accomplish. This is put to advantage in Shapers (where on the forward stroke, a slower motion permits more force, and then there is a quick return on the wasted non-cutting trip. Another place I've see this principle used is on pottery kick-wheels with a lever and connecting rod drive.

Ron,

We are saying the same thing: I never said they necessarily required the same time, quite the opposite.

Your specific application example and explanation better addressed the second part of the OP's question as to where it is used than I did.

Greg

Correct; we are in agreement. I merely replied because I could point out the consequences of an offset, even when displacements are alike, and possibly clarify. Here is another use of the principle: http://www.wfu.edu/~rollins/piston/offset/ . My recollection is that this was used perhaps 80 - 90 years ago, and that the term "dressage" was applied, supposedly to be analogous to the sideways motion of a competition horse. But I haven't found confirmation of that . . .

Ron,

Nice link!

Greg