Marvelous Mechanisms: The Ubiquitous Four Bar Linkage

The four bar linkage is a type of mechanical linkage that is used in many different devices. A few examples are: locking pliers, bicycles, oil well pumps, loaders, internal combustion engines, compressors, and pantographs. In biology we can also find examples of this linkage, as in the human knee joint, where the mechanism allows rotation and keeps the two legs bones attached to each other. It is also present in some fish jaws that evolved to take advantage of the force multiplication that the four bar mechanism can provide.

How It Works

Deployable mirror with scissor linkages. By [Catsquisher] via Wikimedia Commons
The study of linkages started with Archimedes who applied geometry to the study of the lever, but a full mathematical description had to wait until the late 1800’s, however, due to the complexity of the resulting equations, the study and design of complex linkages was greatly simplified with the advent of the digital computer.

Mechanical linkages in general are a group of bodies connected to each other to manage forces and movement. The bodies, or links, that form the linkage, are connected to each other at points called joints. Perhaps the simplest example is the lever, that consists of a rigid bar that is allowed to pivot about a fulcrum, used to obtain a mechanical advantage: you can raise an object using less force than the weight of the object.

Two levers can be connected to each other to form the four bar linkage. In the figure, the levers are represented by the links a (A-D) and b (B-C).  The points A and B are the fulcrum points.  A third link f (C-D) connects the levers, and the fourth link is the ground or frame g (A-B) where the mechanism is mounted. In the animation below, the input link a (the crank) performs a rotational motion driving the rocker rod b and resulting in a reciprocating motion of the link b (the rocker).

This slider-crank arrangement is the heart of the internal combustion engine, where the expansion of gases against a sliding piston in the cylinder drives the rotation of the crank. In a compressor the opposite happens, the rotation of the crank pushes the piston to compress the gas in the cylinder. Depending on how the mechanism is arranged, it can perform the following tasks:

  • convert rotational motion to reciprocating motion, as we just discussed above.
  • convert reciprocating motion to rotational motion, as in the bicycle.
  • constrain motion, e.g. knee joint and car suspension.
  • magnify force, as in the parrotfish jaw.
Locking pliers mechanism. Image from [Engineering made easy]

Some Applications

One interesting application of the four bar linkage is found in locking pliers. The B-C and C-D links are set at an angle close to 180 degrees. When force is applied to the handle, the angle between the links is less than 180 (measured from inside the linkage), and the resulting force in the jaws tries to keep the handle open. When the pliers snap into the locked position that angle becomes less than 180, and the force in the jaws keeps the handle in the locked position.

In a bicycle, the reciprocating motion of the rider´s legs is converted to rotational motion via a four bar mechanism that is formed by the two leg segments, the bicycle frame, and the crank.

An example from nature, the Moray eel. Image from [Matthew West]
As with many other inventions of humankind, we often find that nature has already come up with the same idea via evolution. The parrotfish lives on coral reefs, from which it feeds, and has to grind the coral to get to the polyps inside. For that job, they need a very powerful bite. The parrotfish obtains a mechanical advantage to the muscle force by using a four bar linkage in their jaws! Other species also use the same mechanism, one is the Moray eel, shown in the image, which has the very particular ability to launch its jaws up in the mouth to capture its prey, much like the alien from the film series.

The joints connecting the links in the linkage can be of two types. A hinged joint is called a revolute, and a sliding joint is called a prismatic. Depending on the number of revolute and prismatic joints, the four bar linkage can be of three types:

  • Planar quadrilateral linkage formed by four links and four revolute points. This is shown in the animation above.
  • Slider-crank linkage, formed by three revolute joints and a prismatic joint.
  • Double slider formed by two revolute joints and two prismatic joints. The Scotch yoke and the trammel of Archimedes are examples.

There are a great number of variations for the four bar linkage, and as you can guess, the design process to obtain the forces and movements that we need is not an easy task. An excellent resource for the interested reader is KMODDL (Kinematic Models for Design Digital Library) from Cornell University. Other interesting sites are the 507 mechanical movements, where you can find nice animations, and [thang010146]’s YouTube channel.

We hope to have piqued your curiosity in mechanical things. In these times of ultra fast developments in electronics, looking at the working of mechanisms that were developed centuries ago, but are still present and needed in our everyday lives can be a rewarding experience. We plan to work on more articles featuring interesting mechanisms so please let us know your favorites in the comments below.

Design Analysis: Core XY vs H-Bot

Hackaday writer [Joshua Vasquez] wrote about the mechanical difference between the Core-XY and H-Bot movements commonly used in 3D printers on his personal website. There are so many things a beginning mechanical designer can overlook when setting out to make a movement. Sometimes,in the case of these movements, they aren’t readily apparent, and like finding a troublesome pattern in code; have to be shown before the mind picks them up in future designs.

[Joshua] starts by describing how each movement works. At first glance, the H-Bot movement seems simpler and more effective than the Core-XY.  The Core-XY uses more belting, and some of the pulleys are out of plane with each other. However, this is done to eliminate a moment put on the frame in the H-Bot design. This moment can throw off the accuracy of the movement in unpredictable ways.

The Core-XY movement is one of our favorites. It keeps the motors stationary. It’s compact, precise, repeatable, and linear. It’s good to understand the mechanical reasons for this. Just like learning the SQL database calls a library has been obfuscating for you lets you write better code.

2,100 Mechanical Mechanisms

[Nguyen Duc Thang]’s epic 2100 Animated Mechanical Mechanisms is one of the best YouTube channels we’ve ever seen. A retired mechanical engineer, [Nguyen Duc Thang] has taken on an immense challenge: building up 3D models of nearly every imaginable mechanism in Autodesk Inventor, and animating them for your amusement and enlightenment. And, no, we haven’t watched them all for you, but we’re confident that you’ll be able to waste at least a couple of hours without our help.

If you’re actually looking for something specific, with this many mechanisms demonstrated, YouTube is not the perfect lookup table. Thankfully, [Nguyen Duc Thang] has also produced a few hundred pages of documentation (PDFs, zipped) to go along with the series, with each mechanism classified, described, and linked to the video.

This is an amazing resource as it stands, and it’s probably a good thing that we don’t have access to the 3D files; between the filament cost and the time spent shepherding our 3D printer through 2,100 mechanisms, we’d be ruined. Good thing we don’t know about the Digital Mechanism and Gear Library or KMODDL.

Thanks [alnwlsn] for the tip!
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Continuing Education via Wheel Balancing

There’s an old saying that you should make things twice. Once to figure out how to build the thing, and again to build it the right way. [Pmbrunelle] must agree. His senior project in college was a machine to balance wheels. It was good enough for him to graduate, but he wanted it to be even better.

The original machine required observation of measurements on an oscilloscope and manual calculations. [Pmbrunelle] added an AVR micro, a better motor drive, and made a host of other improvements. As you can see in the video below, the machine works, but [Pmbrunelle] still wasn’t happy.

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How Retractable Pens Work

[Bill Hammack], aka the [EngineerGuy] is at it again, this time explaining how retractable ballpoint pens work.

pen-thumbIn this excellent video, he describes the simple (but remarkably sophisticated) engineering of the mechanism that allows a pen to pop the ballpoint mechanism out, then back in again. It is a great example of how to illustrate and explain a complex concept, much like his videos on how the CCD sensor of your camera works.

Perhaps the most interesting part of the video is an off the cuff observation he makes, though. The Parker company, who first developed the retractable mechanism, were worried that this new design might flop. So they didn’t put the distinctive Parker arrow clip onto the pen until a few years later, when the pen was a big seller. It seems that while some engineering problems are easy to solve, short-sighted accountants are a harder problem.

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Chicken-powered Pendulum

Every once in a while we get sent a link that’s so cute that we just have to post it. For instance: this video from [Ludic Science]. It’s a wind-up chicken toy that kicks a pendulum back and forth. No more, no less.

But before you start screaming “NOT A HACK!” in the comments below, think for a second about what’s going on here. The bird has a spring inside, and a toothed wheel that is jammed and released by the movement of the bird’s foot (an escapement mechanism). This makes the whole apparatus very similar to a real pendulum clock.

Heck, the chick toy itself is pretty cool. It’s nose-heavy, so that under normal conditions it would tip forward. But when it’s wound up, tipping forward triggers the escapement and makes it hop, tipping it backward in the process and resetting the trigger. The top-heavy chicken is an inverted pendulum!

And have a look, if you will indulge, at the very nice low-tech way he creates the pivot: a bent piece of wire, run through a short aluminum tube, held in place by a couple of beads. Surely other pivots are lower-friction, but the advantage of using a rod and sleeve like this is that the pendulum motion is constrained to a plane so that it never misses the chicken’s feet.

Our only regret is that he misses (by that much) the obvious reference to a “naked chick” at the end of the video.

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Bike Pedals in Both Directions, Gets You to Your Destination AND Back

[punamenon2] has built an interesting bike that moves forward regardless if it is pedaled forward or backwards! What? Yes, you read that correctly. Pedal forward or backwards and the bike goes forward. This project started off as any old cruiser with a free-wheeling rear hub. To pull off this mod a second free-wheel and sprocket had to be added to the current wheel assembly. One free-wheel and sprocket set is used when pedaling forward, the other set is used when pedaling in reverse. There is also a new chain tensioner that serves to not only keep the chain taut but also allows for the chain to change directions which ultimately allows this novel idea to work.

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