How does a design go from the computer screen to something you hold in your hand? Not being able to fully answer this question is a huge risk in manufacturing because . One of the important tools engineers use to ensure success is Geometric Dimensioning and Tolerancing (GD&T).
A good technical drawing is essential for communicating your mechanical part designs to a manufacturer. Drafting, as a professional discipline, is all about creating technical drawings that are as unambiguous as possible, and that means defining features explicitly. The most basic implementation of that concept is dimensioning, where you state the distance or angle between features. A proper technical drawing will also include tolerances for those dimensions, and I recently explained how to avoid the pitfall of stacking those tolerances.
Dimensions and tolerances alone, however, don’t tell the complete story. On their own, they don’t specify how closely the geometric form of the manufactured part needs to adhere to your perfect, nominal representation. That’s what we’re going to dig into today with GD&T.
Like many stories, this one started on the roof. This particular roof is located in Michigan and keeps the rain and snow off of the i3Detroit hackerspace. Being an old industrial building, things up on the roof can start getting creaky, and when an almighty screech started coming from one of the rooftop vents as it swiveled in the wind, Nate, one of the group’s coordinators, knew it was time to do something about it.
Previous attempts to silence the banshee with the usual libations had failed, so Nate climbed up to effect a proper repair with real bearings. He dug into the unit, measured for the bearing, and came down to order the correct items. That’s when it struck him: How many should I order? After all, bearings are useful devices, not just to repair a wonky vent but especially handy in a hackerspace, where they can be put to all sorts of uses. Would extra bearings be put to good use, or would they just sit on a shelf gathering dust?
That’s when Nate dropped us a line and asked a question that raises some interesting possibilities, and one which we couldn’t answer offhand: Is there a readily accessible online library of common mechanical parts?
If you’re interested in 3D printing or CNC milling — or really any kind of fabrication — then duplicating or interfacing with an existing part is probably on your to-do list. The ability to print replacement parts when something breaks is often one of the top selling points of 3D printing. Want some proof? Just take a look at what people made for our Repairs You Can Print contest.
Of course, to do that you need to be able to make an accurate 3D model of the replacement part. That’s fairly straightforward if the part has simple geometry made up of a primitive solid or two. But, what about the more complicated parts you’re likely to come across?
In this article, I’m going to teach you how to reverse engineer and model those parts. Years ago, I worked for a medical device company where the business model was to duplicate out-of-patent medical products. That meant that my entire job was reverse engineering complex precision-made devices as accurately as possible. The goal was to reproduce products that were indistinguishable from the original, and because they were used for things like trauma reconstruction, it was critical that I got it right.
Most of us are more bits-and-bytes than nuts-and-bolts, but we have the deepest appreciation for the combination of the two. So, apparently, does [rectorsquid]. Check out the design and flow of his rolling ball sculpture (YouTube, embedded below) to see what we mean. See how the arms hesitate just a bit as the ball is transferred? See how the upper arm gently places it on the ramp with a slight downward gesture? See how it’s done with one motor? There’s no way [rectorsquid] designed this on paper, right?
Of course he didn’t (YouTube). Instead, he wrote a simulator that lets him try out various custom linkages in real time. It’s a Windows-only application (sigh), but it’s free to use, while the video guides (more YouTube) look very comprehensive and give you a quick tour of the tool. Of special note is that [rectorsquid]’s software allows for sliding linkages, which he makes very good use of in the rolling ball sculpture shown here.
We’ve actually secretly featured [rectorsquid]’s Linkage software before, in this writeup of some amazing cosplay animatronic wings that used the program for their design. But we really don’t want you to miss out if you’re doing mechanical design and need something like this, or just want to play around.
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.
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.
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.
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.
[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.