# Introduction to Mechanisms

Yi Zhang
with
Susan Finger
Stephannie Behrens

This mechanism has three moving links. Two of them are pinned to the frame, which is not shown in this picture. In SimDesign, you can nail these two links to the background.

How many degrees of freedom (DOF) does this mechanism have? If it has one, you can impose one constraint on the mechanism for it to have definite motion. For example, you can pull the nailed link on the left (making it the input link) and it will turn around the nail. The right link (now the output link) will make an oscillating motion. Suppose you put a pen on the top of the triangle-shaped link. (The triangle is also called a link. A link is not necessarily a simple line-shaped body). The pen will trace its path. The triangle-shaped link connects the two moving pivots and couples the input and the output motion; hence, it is called coupler.

Linkages have different functions. The functions are classified depending on the primary goal of the mechanism:

• Function generation: the relative motion between the links connected to the frame,
• Path generation: the path of a tracer point, or
• Motion generation: the motion of the coupler link.

#### 1.1.1 Crane

An application of path generation is a crane in which an approximate horizontal trace is needed.

#### 1.1.2 Hood

An example of motion generation is a hood which opens and closes.

#### 1.1.3 Parallelogram mechanism

In a parallelogram four-bar linkage, the orientation of the coupler does not change during the motion. The figure illustrates a loader.

### 1.2 Slider-crank mechanisms

The four-bar mechanism has some special configurations created by making one or more links infinite in length. The slider-crank (or crank and slider) mechanism shown below is a four-bar linkage with a slider replacing an infinitely long output link.

Pull the crank of this mechanism and you will see that it transfers rotary motion into translation. Most mechanisms are driven by motors, and slider-cranks are often used to transform rotary motion into linear motion.

#### 1.2.1 Crank and piston

You can also use the slider as the input link and the crank as the output link. In this case, the mechanism transfers translational motion into rotary motion. The pistons and crank in an internal combustion engine are an example of this type of mechanism. The corresponding SimDesign file is mechanisms/combustion.sim.

You might wonder why there is another slider and a link on the left. This mechanism has two dead points. The slider and link on the left help the mechanism to overcome these dead points.

#### 1.2.2 Block feeder

One interesting application of slider-crank is the block feeder. The SimDesign file can be found in mechanisms/block.feeder.sim

## 2. Cam mechanisms

Linkages, while useful, cannot achieve all possible motions. For example, if the output link must remain stationary for a certain period of time while the input link keeps turning, linkages cannot be used. Cam mechanisms can realize any required output motion. The composition of a cam mechanisms is simple: a cam, a follower and a frame. (You may find springs used in a cam mechanism to keep the follower and the cam in contact, but it is not part of the cam mechanism.)

#### 2.1 Rotating cam/Translating follower

If you turn the cam, the follower will move. The weight of the follower keeps them in contact. This is called a gravity constraintcam.

#### 2.2 Rotating cam/Rotating follower

The SimDesign file is mechanisms/cam.oscillating.sim. Notice that a roller is used at the end of the follower. In addition, a spring is used to maintain the contact of the cam and the roller.

If you try to calculate the degrees of freedom (DOF) of the mechanism, you must imagine that the roller is welded onto the follower because turning the roller does not influence the motion of the follower.

## 3. Gears

There are many kinds of gears. The following examples are involute spur gears. We use the word involute because the contour of gear teeth curves inward. There are many terminologies, parameters and principles for gears. One of the important concept is the velocity ratio, which is the ratio of the rotary velocity of the driver gear to that of the driven gears.

The number of teeth in these gears are 15 and 30, respectively. If the 15-tooth gear is the driving gear and the 30-teeth gear is the driven gear, their velocity ratio is 2.

An example of a set of gears is in mechanisms/gear10.30.sim.

### 3.1 Rack and pinion

When the number of teeth of a gear becomes infinite, the center of the gear goes to infinity. The gear becomes a rack. The following picture shows a rack and pinion. The corresponding SimDesign file is mechanisms/gear.rack.sim.

You can pull the pinion so that it turns and drives the rack. You can also pull the rack along the guide and drive the pinion.

### 3.2 Ordinary gear trains

Gear trains consist of two or more gears that transmit motion from one axis to another. Ordinary gear trains have axes, relative to the frame, for all gears comprising the train.

### 3.3 Planetary gear train

The SimDesign file is mechanisms/gear.planet.sim. Since the sun gear (the largest gear) is fixed, the DOF of the above mechanism is one. When you pull the arm or the planet, the mechanism has a definite motion. If the sun gear isn't frozen, the relative motion is difficult to control.

## 4. Miscellaneous mechanisms

### 4.1 Ratchet mechanism

A wheel with suitably shaped teeth, receiving an intermittent circular motion from an oscillating member, is a ratchet wheel. The figure below shows a simple ratchet mechanism.

A is the ratchet wheel, and B is an oscillating link. Attached to B is a pawl which is a link designed to engage with the ratchet teeth to prevent the wheel from moving in one direction. This mechanism has a supplementary pawl at D. When the link B moves in a counterclockwise direction, the pawl C pushes the wheel through a partial rotation. When the link B moves clockwise, the pawl C slides over the points of the teeth while the wheel remains at rest because of the fixed pawl D. The amount of backward motion possible varies with the pitch of the teeth. The smaller the teeth, the smaller the backward motion. The contact surfaces of wheel and pawl should be inclined so they don't disengage under pressure.

The corresponding SimDesign file is mechanisms/ratchet.sim. The four-bar linkage on the right generates an oscillating rotation for link B. Pull the crank to watch the ratchet work.

### 4.2 Geneva Wheel

An interesting example of intermittent gearing is the Geneva Wheel.

In this mechanism, for every turn of the driver wheel A, the driven wheel B makes a quarter turn. The pin, attached to driver wheel A, moves in the slots causing the motion of wheel B. The contact between the lower part of driver A with the corresponding hollow part of wheel B, retains it in position when the pin is out of the slot. Wheel A is cut away near the pin as shown, in order to provide clearance for wheel B as it moves. If one of the slots is closed, A can make less than one revolution in either direction before the pin strikes the closed slot, stopping the motion. Early watches, music boxes, etc., used Geneva wheels to prevent over winding. From this application, they also are called Geneva Stops. As a stop, wheel A is fastened to the spring shaft, and B turns on the axis of the spring barrel. The number of slots in B depends upon the number of times the spring shaft should be turned.

The SimDesign file for Geneva wheel is "geneva.sim".

You may try this mechanism by pulling on the Geneva wheel.