# 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

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.

## 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.

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.

# Animatronic Cosplay Wings

In recent years, Cosplay as a hobby has seen improvement in the props department by leaps and bounds. Thanks in part due to the rise of the Maker culture and the easy availability of design and manufacturing tools and processes. Case in point is this awesome set of Animatronic Wings that programmer [Nelson Stoldt] built for his daughter who wanted to be Nightmare Moon.

[Nelson] had no idea what he’d gotten himself in to when he answered “Sure, I can do that”. Making motorized cosplay wings that open up to 8 feet wide and close again at the flick of a switch without weighing a ton is not a trivial project. The final rig did end up tipping the scales at just over 9 kgs, but we guess that’s a load that Cosplayers are used to hauling around.

Using a nifty program called Linkage, he played around with a few different design approaches until he found a mechanism that worked well. If you ever want to build one of [Theo Jansen]’s Strandbeest, give this program a spin. Armed with this information, and a spreadsheet to help determine the exact length of each linkage element, he modelled the project in Sketchup. The wings are operated by a scissor mechanism that is driven by a motorized screw operated sliding carriage. Wing position is measured by a potentiometer coupled to one of the wing elements. Basically, he just built a huge, powerful servo.

# UAV Coaxial Copter Uses Unique Drive Mechanism

Personal UAV’s are becoming ubiquitous these days, but there is still much room for improvement. Researchers at [Modlab] understand this, and they’ve come up with a very unique method of controlling pitch, yaw, and roll for a coaxial ‘copter using only the two drive motors.

In order to control all of these variables with only two motors, you generally need a mechanism that adjusts the pitch of the propeller blades. Usually this is done by mounting a couple of tiny servos to the ‘copter. The servos are hooked up to the propellers with mechanical linkages so the pitch of the propellers can be adjusted on the fly. This works fine but it’s costly, complicated, and adds weight to the vehicle.

[Modlab’s] system does away with the linkages and extra servos. They are able to control the pitch of their propellers using just the two drive motors. The propellers are connected to the motors using a custom 3D printed rotor hub. This hub is specifically designed to couple blade lead-and-lag oscillations to a change in blade pitch. Rather than drive the motors with a constant amount of torque, [Modlab] adds a sinusoidal component in phase with the current speed of the motor. This allows the system to adjust the pitch of the blades multiple times per rotation, even at these high speeds.

Be sure to watch the demonstration video below. Continue reading “UAV Coaxial Copter Uses Unique Drive Mechanism”

# Improving a hexapod design

[JC] built himself a hexapod based on a project he found on the Internet. It worked fairly well, but was mechanically weak and prone to breakage. He set out to improve the design and came up with the unit seen above. It uses three servo motors to control the six legs, and walks quite well as seen in the quick clip after the break. It’s not quite as agile as the little acrobatic six-legger we saw yesterday, but the movement is quite pleasing and it’s capable of moving forward, backward, and turning. [JC’s] post is four pages in all so don’t forget to seek out his links for the construction, linkage, and servo control pages to find concept drawings, cad designs, and his thoughts on the process.

# Four generations of motion simulators

We like a good flight simulator but often find the available control schemes lacking. [Roland] not only builds his own controls, but creates full cockpits that add physical motion to the mix. He completed his third generation cockpit last year.  It’s pictured above as well as in video after the break. That design uses a belt system to move the tricked out cockpit.

Now he’s started work on prototypes for generation IV. This time he’s using three Sarrus linkages to replace the belt system.  We saw these linkages yesterday in an extruder prototype and if they can handle the load they should work well for this application. Video of the prototype is embedded after the break but be warned, the lewd thrusting motions are not for the faint-of-heart. Continue reading “Four generations of motion simulators”