Table of Contents

1. Linkage mechanisms

(of Mechanisms) / AT Determining Mobility or DOF Grubler & Kutzbach Equations Lower pairs (first order joints) or full-joints (counts as J = 1in Gruebler’s Equation) have one degree of freedom (only one motion can occur): –-Revolute (R): Also called a pin joint or a pivot, take care to ensure that the.

1.1 Four bar linkages

1. The pin-slot joint is one of the most commonly used form of kinematic pairs, which with clearance will have a significant effect on the motion and dynamic response of multibody systems. In this study, the multibody system with a pin-slot clearance joint is modeled and the kinematic and dynamic effects are studied. Firstly, the generalized coordinate systems were established and the motion.
2. He discovered that one of the gears at the back of the Mechanism, mounted on this large 223-tooth gear, had a pin in it. MICHAEL WRIGHT: This is the pin and slot mechanism. There's a wheel in the.

Linkage are composed of links andlower pairs. The simplestclosed-loop linkage is the four-bar linkage, which has three movinglinks, one fixed link and four pin joints. A linkage with one linkfixed is a mechanism. You can load the following four-barlinkage into SimDesign from the file mechanisms/fourbar.sim.

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

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

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

• Function generation: the relative motion between the linksconnected 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 approximatehorizontal 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 bymaking one or more links infinite in length. The slider-crank (or crank andslider) mechanism shown below is a four-bar linkage with a slider replacingan infinitely long output link.

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

1.2.1 Crank and piston

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

You might wonder why there is another slider and a link on theleft. This mechanism has twodead points. Theslider and link on the left help the mechanism to overcome these deadpoints.

1.2.2 Block feeder

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

2. Cam mechanisms

Linkages, while useful, cannot achieve all possible motions. Forexample, if the output link must remain stationary for acertain period of time while the input link keeps turning, linkagescannot be used. Cam mechanisms can realize any required outputmotion. The composition of a cam mechanisms is simple: a cam, afollower and a frame. (You may find springs used in a cam mechanism tokeep the follower and the cam in contact, but it is not part of thecam mechanism.)

2.1 Rotating cam/Translating follower

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

2.2 Rotating cam/Rotating follower

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

If you try to calculate the degrees offreedom (DOF) of the mechanism, you must imagine that the rolleris welded onto the follower because turning the roller does notinfluence the motion of the follower.

3. Gears

There are many kinds of gears. Thefollowing examples are involute spur gears. We use the wordinvolute 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 isthe ratio of the rotary velocity of the driver gear to that of thedriven gears.

The number of teeth in these gearsare 15 and 30, respectively. If the 15-tooth gear is the driving gearand 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 ofthe gear goes to infinity. The gear becomes a rack. The followingpicture shows a rack and pinion. The corresponding SimDesign file ismechanisms/gear.rack.sim.

You can pull the pinion so that it turns and drives the rack. Youcan 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 fromone axis to another. Ordinary gear trains have axes, relative to theframe, for all gears comprising the train.

3.3 Planetary gear train

The SimDesign file is mechanisms/gear.planet.sim. Since the sungear(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 definitemotion. If the sun gear isn't frozen, the relative motion isdifficult to control.

4. Miscellaneous mechanisms

4.1 Ratchet mechanism

A wheel with suitably shaped teeth, receiving an intermittent circularmotion from an oscillating member, is aratchet wheel. The figure below shows a simple ratchetmechanism.

Mechanism Pin Slot Lock

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

The corresponding SimDesign file is mechanisms/ratchet.sim. Thefour-bar linkage on the right generates an oscillating rotation forlink 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 drivenwheel B makes a quarter turn. The pin, attached to driver wheel A,moves in the slots causing the motion of wheel B. The contact betweenthe lower part of driver A with the corresponding hollow part of wheelB, retains it in position when the pin is out of the slot. Wheel A iscut away near the pin as shown, in order to provide clearance forwheel B as it moves. If one of the slots is closed, A can make lessthan one revolution in either direction before the pin strikes theclosed 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 tothe spring shaft, and B turns on the axis of the spring barrel. Thenumber of slots in B depends upon the number of times the spring shaftshould be turned.

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

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

Mechanism Pin Slot Machine

• 1. Linkage mechanisms
  • 1.1 Four bar linkages
  • 1.2 Slider-crank mechanisms
• 2. Cam mechanisms
• 3. Gears
• 4. Miscellaneous mechanisms

Pin In Slot Mechanism