What is a coordinate system? Why is there more than one option? What is a coordinate system? I described this as how the three-dimensional space is understood by the machine, how a position and a movement between each position can be plotted. If you take a piece of graph paper and you draw it pair of x- and y-axis on it, you can define any position on the piece of paper by using a value on the x-axis and a value on the y-axis. Moving from one position to another can be solved not only by delivering a new pair of coordinates, but also by changing information for the movement. For example, move 10 units further along the x-axis and three units back along the y-axis The coordinate system, the mathematical contexts for moves and positions, is not a piece of hardware. But without this element clearly established, the machine wouldn't have the ability to execute the long sequential sets of instructions delivered to it in the job file from the slicing process. The job file includes thousands and thousands of simple moves that together with the activity of the extrusion system delivers the right amount of plastic to the right position. But are there other means of noting positions and moves? The Cartesian coordinate system you are familiar with from simple two-axis graphs is just one of several options. Depending on how the machine you're running was constructed and the kinds of instructions that are expected, there can be reasons to pick another coordinate system entirely. Here's a metaphor to help you see how you can accomplish similar positions and movements by using other criteria and tools. Think of taking a GPS location tracker on a hike. Comparing where you are on the ground to where you are on a map is a matter of looking at the latitude and longitude reference on the GPS device and finding the corresponding position on the map. Pretty much and straightforward, a Cartesian coordinate system has the XY axis graph paper model. However, what if your GPS device couldn't report longitude and latitude, I could only instead report elevation and a distance from a known marker? Evaluating the data on the GPS device, you could still find your position and route along a topographical map, but you would be working with that map in a very different way. Let's review the most common coordinate systems in use within desktop 3D printing hardware. Cartesian coordinate system. This is the most popular coordinate system which tends to be the most intuitive for users. Positions in three-dimensional space are recorded within a rectilinear grid in terms of X, Y, and Z values with X and Y as the positions within each layer and Z is the height above the build platform. Many Cartesian machines are built in a way that reflects this with means of moving the toolhead in X and Y and toolhead on the Z. Different desktop models put the origin, i.e 000 for X, Y, and Z, in different positions with the two most popular positions being the front left corner of the build platform so that the values both X and Y are always positive and the dead middle of the platform, making it easy to position an object right at the center and easy to offset it in terms of either the X or Y direction in terms of that popular center position. As with the GPS coordinates, there is an intuitive relationship between a point in the platform and a position requested in a job file. For example, a job file instruction to move 13 millimeters over to the right and 10 millimeters forward to reach next position. Because of this, a number of mechanical arrangements and mechanical distributions that behave differently from typical Cartesian machines still use Cartesian coordinate system to record and process positions. Most Delta printers, for example, process Cartesian coordinate based G-Code job files that the onboard firmware and electronics convert on the fly to the multiple instructions per command for the carriage movement on the A, B, and C towers. Polar coordinate system. Another coordinate system that is occasionally used is the polar coordinate system. This is a bit more similar to the elevation plus distance from a known marker reference that I made at the start of this lecture when we were talking about position tracking on a hike. Less intuitive than the Cartesian coordinate system, but the math works out fine. With a polar coordinate system, points are plotted on a circular grid in terms of distance out from the center instead of using a square grid. While the hiking metaphor might make this seem like a hassle, it helps to consider that the polar coordinate printers are also typically polar in their mechanical arrangement. Having a build platform that spins so that moving a distance can be more clearly understood as moving clockwise or counterclockwise while moving in towards or out away from the center. Why think this way? We will address this when we talk about polar mechanical arrangements, how this approach allows for a large printable area for a fewer number of actuators than the other styles. Other coordinate systems. While the use of other coordinate system options exists and has been popular enough in other computer-guided fabrication systems, such as multi-access robotic arms, CNC lathes and more, there really aren't enough examples of patterns of use of exotic coordinate systems and system hybrids in detail beyond just mentioning that it is possible to use cylindrical, spherical, and complex kinematics and inverse kinematics guidance coordinate systems for desktop 3D printers. Also worth mentioning, SCARA style fabrication robots can sometimes use combinations of Cartesian coordinates for the movement of the robot itself and polar or rotary coordinates for arms and tools. Also worth mentioning, SCARA style fabrication robots can sometimes use combinations of Cartesian coordinates for movement of the robot itself and polar or rotary coordinates for arms and tools to reduce the motion interpolation load for resolving both linear and circular interpolation at the same time. To reduce the motion interpolation load for resolving both linear and circular interpolation at the same time. Likewise, certain implementations of six-axis arms can also draw on unique coordination systems for encoding job instructions. Though the you use of motion guidance systems that can resolve Cartesian instructions is even more common. We'll explore these types of robots more in terms of mechanical arrangements. The origin. The key component of the mechanical system where the coordinate system and the physical hardware come together is at the origin. This is the machine origin position, what I described as a 000 position as it often is noted when using a Cartesian coordinate system. There are other origin positions evolved in the process of design for 3D printer. The design software origin which is a key value referenced in the 3D model file that identifies where each of the geometry is located, or at least that drives a series of relationships that produces the intended design. There is also an initial position that the 3D printer control software uses when importing a mesh and placing it within the virtual build environment. This can sometimes be a very different orientation then used by the design software, requiring the operator to flip the object on one or more access to establish the intended fabrication orientation. The machine origin is a position established at the beginning of a print that makes it possible for the motion mechanical subsystem to follow the long sequential set of movement instructions in the job file. But it is the coordinate system that makes sure that the virtual model used to create the job file instructions matches the real-world positions achieved by the motion mechanical system. In practice, many machine designers for Cartesian style machines in terms of mechanical arrangement, the most common type, will put the origin in the bottom front left corner to eliminate the need for negative values in X, Y, and Z and Delta style printers who often place the origin at the dead center of a cylindrical built area. Endstops. The physical hardware that makes it possible to establish that origin position are the endstops, which are the mechanical sensors position within the machine that are each to be triggered in the first stage of the 3D printing process during activity called homing.The breakout endstop boards reports back to the main board at the precise moment that a moving element of the machine triggers the endstop. From that point forward, the physical position of the mechanism in reference to the motor position is known. Counting x number of steps forward or back on that axis indicated by the job file referencing the known value of steps per millimeter brings together the path planning established by the slicer with the physical machine. It is worth noting here that this technique is not without its limits, and no amount of precision for determining initial position will help you if the number of steps counted by each separate motor are locked to different links or produce a different than expected translation. Thanks to mechanical binding or obstacles along the way. Triggering the homing process. Triggering the homing process. Moving the toolhead and/or platform into position that makes contact with and trigger the electronic endstops is the most important preprinting step for desktop 3D printers that are open loop, as in machines that do not have constant telemetry feed back from stepper motors, motion controllers, velocity, and gyroscopic motion detection. This is a common strategy for robotics and automation in general because installing all of the systems involved with a fully closed feedback loop is not always warranted for every mechanical process. Closed loop motion control systems can be extremely expensive and time-consuming to set up. One of the main reasons that both desktop and industrial 3D printers tend to be cheaper than the use of robots task to the same fabrication process are the cost savings involved with eliminating any superfluous systems, sensors, and processor component. Because computer-guided fabrication equipment addresses an area within the control of the equipment, more assumptions can be safely made than an automation system in addressing an environment that is constantly on the flux. This homing process establishes known positions within each moving mechanical component, such that all of the path instructions in the job file that follow can be executed correctly and precisely. To remember what this process is called and how it functions, imagine that you wake up with most of your senses masked, uncertain where you are, but needing to retrieve something from your kitchen. Without any means to establish where you are located and how you are positioned there, how on earth would you ever accomplish your goal? The homing process acts much the same way as putting your hand on your front door knob. You think, "I know where I am and how I can get to where I need to go." Though, unlike your desktop 3D printer, you probably rely much more on closed-loop feedback as you move through your environment, i.e actively looking around and assessing where you are, instead of memorizing the floor plan.
