OBJECTIVES:

• To gain a more intuitive understanding of four-bar mechanisms by doing a hands-on approach.
• To investigate four-bar mechanism parameters (e.g. Grashof condition, toggle points, transmission angle).

BACKGROUND:

A Grashof mechanism exists when a four-bar mechanism meets the following criterion:
                    s + l <= p + q
where:

	s:	length of shortest link
	l:	length of longest link
	p,q:	lengths of intermediate links

If this condition is met, at least one link will be capable of making a full revolution with respect to the ground link.  Otherwise, no link will be capable of a complete revolution relative to any other link.

If a link is capable of making a complete revolution, it is termed a crank. If it can only oscillate back and forth, it is a rocker. Note - the terms "crank" and "rocker" usually apply only to links pivoted to ground, but they can also be used to describe a complex-motion link (e.g., a coupler), based on whether or not the link can make a complete revolution.

A toggle position occurs when two of the moving links are collinear (linkage forms a triangle such as A'B'C'). When in a toggle position, the linkage will not allow further input motion in one direction from one of the rockers.

The transmission angle (μ) is the angle between the lines of action of the output link (C) and the coupler (B). It is always positive, and always acute (less than 90 degrees).  It is mainly used for calculating the amount of force transferred to the output link from the driving link (A).

An inversion occurs when a different ground link is chosen for the mechanism. Thus there are as many inversions for a given linkage as there are links.

PROBLEM STATEMENT:
Build cardboard models of the linkages and describe the motions of each inversion.  As a guideline, lengths are in inches but any scale you want to use is fine (just not too small or too big).

MATERIAL AND METHODS:
You will need (to be provided by the TAs):

1. thick poster board for cutting out links
2. scissors
3. ruler
4. protractor
5. thumb tacks to serve as pivots
6. foam board to allow the fixed pivots to be held down

It's suggested you bring your own scissors, ruler, and protractor so you don't have to wait for others to finish using the few sets that will be provided.  Also, if you don't already have a protractor and compass, you might want to buy them; they will definitely come in handy for future homework.

Cut out strips (1/2-1" thick) of poster board in lengths as defined in the problem statement.  You may want to cut them a little longer than the length suggested so that you can tack them at the specified lengths (i.e., cut a "two-inch" bar 2-1/2 inches and tack it 1/4" from each end).  Assemble the "bars" using the thumbtacks (down into the foam board for fixed pivots and up for moving pivots), leaving them free to rotate.  For consistency, join W to X to Y to Z to W.  Play around with the mechanism investigating inversions, toggle positions, transmission angles, and so on.  Complete the lab worksheet.

REFERENCES:

• Grashof Criterion Videos - UNLV (www.me.unlv.edu/~mbt/320/Grashof.html)