Articulating apparatus of a waterjet system and related technology

Abstract

A waterjet system in accordance with at least some embodiments includes a carriage, a motion assembly configured to move the carriage horizontally relative to a workpiece, and a cutting head carried by the carriage. The waterjet system can also include a kinematic chain through which the cutting head is operably connected to the carriage. The kinematic chain can include first, second, and third joints rotatably adjustable about different first, second, and third axes, respectively. The carriage and the first and second joints can be configured to move the cutting head along a path relative to the workpiece while the cutting head directs a jet toward the workpiece to form a product. The third joint can be configured to shift a kinematic singularity away from the path to reduce or eliminate delay and corresponding reduced cutting accuracy associated with approaching the kinematic singularity.

Claims

1. A waterjet system, comprising: a carriage; a motion assembly configured to move the carriage in a first horizontal direction relative to a workpiece and a second horizontal direction relative to the workpiece, wherein the second horizontal direction is not parallel to the first horizontal direction; a cutting head carried by the carriage, wherein the cutting head is configured to direct a jet toward the workpiece while the motion assembly moves the carriage horizontally relative to the workpiece; and a kinematic chain through which the cutting head is operably connected to the carriage, wherein the kinematic chain includes— a first joint rotatably adjustable about a first axis, a second joint rotatably adjustable about a second axis different than the first axis, a third joint rotatably adjustable about a third axis different than the first and second axes, wherein the first, second, and third axes are not parallel to each other, and a fourth joint linearly adjustable to move the cutting head vertically relative to the carriage, and wherein— the first joint is in series between the cutting head and the second joint, the second joint is in series between the first joint and the third joint, the third joint is in series between the second joint and the carriage, and the fourth joint is in series between the third joint and the motion assembly.

2. The waterjet system of claim 1 wherein the third axis is perpendicular to the second axis.

3. The waterjet system of claim 1 wherein: the third joint is rotatably adjustable about the third axis to move between a first state and a second state; the second axis is vertical when the third joint is in the first state; and the second axis is not vertical when the third joint is in the second state.

4. The waterjet system of claim 1 wherein the third axis is horizontal.

5. The waterjet system of claim 1 wherein the third joint is a step joint.

6. The waterjet system of claim 1 wherein the third joint is configured to be adjusted manually.

7. The waterjet system of claim 1 wherein the third joint is configured to be adjusted automatically.

8. The waterjet system of claim 1 wherein: the first joint is rotatably adjustable about the first axis within a first range of motion; the second joint is rotatably adjustable about the second axis within a second range of motion greater than the first range of motion; and the third joint is rotatably adjustable about the third axis within a third range of motion less than the first range of motion.

9. The waterjet system of claim 8 wherein the third range of motion is less than or equal to 30 degrees.

10. The waterjet system of claim 8 wherein the third range of motion is less than or equal to 90 degrees.

Description

BRIEF DESCRIPTION OF THE DRAWINGS

(1) Many aspects of the present technology can be better understood with reference to the following drawings. The components in the drawings are not necessarily to scale. Instead, emphasis is placed on clearly illustrating the principles of the present technology. For ease of reference, throughout this disclosure identical reference numbers may be used to identify identical or at least generally similar or analogous components or features.

(2) FIG. 1 is a partially schematic and partially cross-sectional profile view of a waterjet system in accordance with at least some embodiments of the present technology.

(3) FIG. 2 is a profile view of a cutting head and kinematic chain of the waterjet system shown in FIG. 1 with a nozzle of the cutting head in a vertical orientation.

(4) FIG. 3 is a profile view of the cutting head and kinematic chain of the waterjet system shown in FIG. 1 with the nozzle of the cutting head in an off-vertical orientation.

(5) FIG. 4A is a profile view of a cutting head and kinematic chain of a waterjet system in accordance with at least some embodiments of the present technology with a nozzle of the cutting head in a vertical orientation.

(6) FIG. 4B is an enlarged view of a portion of FIG. 4A.

(7) FIG. 5A is a profile view of the cutting head and kinematic chain shown in FIG. 4A with the nozzle of the cutting head in an off-vertical orientation.

(8) FIG. 5B is an enlarged view of a portion of FIG. 5A.

(9) FIGS. 6 and 7 are flow charts illustrating methods for operating a waterjet system in accordance with at least some embodiments of the present technology.

DETAILED DESCRIPTION

(10) Waterjet systems typically include a carriage connected to an x/y motion assembly that precisely positions the carriage in a horizontal plane. The carriage carries a cutting-head assembly including an elongate nozzle through which a waterjet travels axially toward a workpiece. In some waterjet systems, the nozzle is fixedly connected to the carriage such that the carriage can move the nozzle horizontally relative to the workpiece, but the nozzle cannot tilt relative to the workpiece. This type of system is well-suited for making through cuts and straight blind cuts in a stationary workpiece, which may be sufficient to form simple three-dimensional products. Forming complex three-dimensional products, however, typically requires use of a cutting-head assembly that allows the nozzle to tilt relative to a workpiece. Some conventional cutting-head assemblies that allow the nozzle to tilt relative to a workpiece include a kinematic chain with a first joint and a second joint in series between the nozzle and the carriage. The first joint allows the nozzle to rotate within a limited range about an off-vertical axis. The second joint allows the nozzle to rotate 360 degrees about a vertical axis. Together, these joints allow the nozzle to move into any orientation in a spherical sector defined by the range of motion of the first joint.

(11) Conventional two-joint cutting-head assemblies tend to be well-suited for processing that calls for infrequent large (e.g., greater than 30-degree) angular changes in the orientation of the nozzle. These conventional cutting-head assemblies, however, tend to be poorly suited for processing that calls for frequent small (e.g., less than 10-degree) angular changes in the orientation of the nozzle. When the vertical axis of the second joint of a conventional two cutting-head assembly is coincident with the nozzle axis (also the waterjet axis), operating the second joint has no effect on the orientation of the nozzle. This is known as a kinematic singularity. Near this kinematic singularity, the math that conventional waterjet systems use to determine the respective positions of the first and second joints to cause a desired orientation of the nozzle automatically calls for large rotations of the second joint. These large rotations of the second joint tend to be disproportionate to the magnitude of the desired angular change in the orientation of the nozzle. Often, the time required to execute these large rotations of the second joint necessitates a temporarily decrease in cutting speed (i.e., the speed at which the motion system moves the nozzle horizontally). After a large rotation of the second joint is complete, the cutting speed may return to a steady-state speed. This is problematic because waterjet processing is time dependent. Unlike a conventional milling tool (e.g., a grinding head), a waterjet forms a kerf in a workpiece by erosion that progresses laterally to different extents depending on the speed at which the waterjet moves relative to the workpiece. In general, slower cutting speeds correspond to wider kerfs and faster cutting speeds correspond to narrower kerfs. When cutting speed changes to accommodate operation of the second joint of a conventional two cutting-head assembly during operation of the cutting-head assembly near a kinematic singularity, the overall kerf width for a cutting project will be variable. This, in turn, reduces the dimensional accuracy of the product.

(12) Compounding the kinematic-singularity problem is the fact that operating a conventional two-joint cutting-head assembly near the vertical-axis kinematic singularity can be very useful. For example, slightly tilting the nozzle in the direction of travel can increase cutting efficiency. In addition (and usually more importantly) slightly tilting the nozzle away from an adjacent product wall is often the best way to reduce or eliminate undesirable taper. In waterjet processing, taper refers to a difference between the kerf width at the top of a cut and the kerf width at the bottom of the cut. A typical waterjet cut has a slight taper, the most common type being V-shaped taper. V-shaped taper occurs because a waterjet loses some of its cutting energy as it cuts deeper into a workpiece. Slightly more material is removed at the top of the cut where the waterjet enters the workpiece, than at the bottom of the cut where the waterjet exits the workpiece. V-shaped taper is usually associated with fast cutting. In general, the greater the cutting speed, the more pronounced the taper. Slightly tilting the nozzle away from being perfectly aligned with the desired orientation of an adjacent product wall shifts the taper to a scrap wall opposite to the product wall. This offsetting technique is very effective for reducing or eliminating the effect of taper on the dimensional uniformity of the product wall.

(13) The optimum nozzle tilt for reducing taper usually varies over the course of a cutting project. For example, when cutting speed during a cutting project is low (e.g., as the waterjet approaches a corner), the effect of taper may be less pronounced. In contrast, when cutting speed is high (e.g., along a straight cut), the effect of taper may be more pronounced. Accordingly, it can be desirable to reduce nozzle tilt in the former case to avoid overcompensating for the taper, and to increase the nozzle tilt in the latter case to avoid undercompensating for the taper. These changes in nozzle tilt can be called for in any direction depending on the orientation of the product wall adjacent to the waterjet. Cutting speed changes may occur frequently over the course of a cutting project, particularly if the desired product wall has many corners. Furthermore, the optimum nozzle tilt to reduce or eliminate taper is usually less than 10 degrees from the cut surface. A cutting program that includes nozzle tilt to reduce or eliminate taper, therefore, often includes frequent small angular changes in the orientation of the nozzle.

(14) If not for speed-related and taper-related nozzle tilt, most waterjet processing would occur with the nozzle in a vertical orientation to form vertical product walls. Indeed, this is the orientation of the nozzle in most (if not all) waterjet systems in which the nozzle is fixed relative to the carriage. When speed-related and/or taper-related nozzle tilt is/are introduced into a typical cutting project, the specified nozzle tilt tends to be within 10 degrees off vertical. As discussed above, in a conventional two-joint cutting-head assembly, the second joint rotates about a vertical axis that aligns with the nozzle axis at a kinematic singularity. Therefore, implementing speed-related and/or taper-related nozzle tilt with a conventional two cutting-head assembly would involve frequent small angular changes in the orientation of the nozzle near the vertical-axis kinematic singularity. This would be impractical because the cutting speed would need to decrease to allow time for the second joint to make frequent large rotations. The inventors recognized that one approach to addressing this problem is to allow the position of the second axis of a two joint cutting-head assembly to be variable. This reduces kinematic-singularity-related delay in simple cutting projects calling for forming mostly vertical product walls. A problem with this approach, however, is that kinematic-singularity-related delay may still occur in more complex cutting projects calling for forming off-vertical product walls. The inventors further recognized that adding a third joint to the kinematic chain between the nozzle and the carriage would allow kinematic-singularity-related delay to be reduced significantly even in complex cutting projects.

(15) Systems, devices, and methods in accordance with embodiments of the present technology can at least partially address one or more of the problems described above and/or other problems associated with conventional technologies whether or not stated herein. For example, waterjet systems in accordance with at least some embodiments of the present technology have features that facilitate reliably avoiding kinematic-singularity-related delay. Specific details of systems, devices, and methods in accordance with various embodiments of the present technology are disclosed herein with reference to FIGS. 1-7. Although the systems, devices, and methods may be disclosed herein primarily or entirely with respect to waterjet applications, other applications in addition to those disclosed herein are within the scope of the present technology. For example, suitable features of described waterjet systems can be implemented in the context of plasma-cutting systems or other types of beam-cutting systems. Furthermore, it should be understood, in general, that other systems, devices, and methods in addition to those disclosed herein are within the scope of the present technology. For example, systems, devices, and methods in accordance with embodiments of the present technology can have different and/or additional configurations, components, and procedures than those disclosed herein. Moreover, a person of ordinary skill in the art will understand that systems, devices, and methods in accordance with embodiments of the present technology can be without one or more of the configurations, components, and/or procedures disclosed herein without deviating from the present technology.

(16) Waterjet systems in accordance with at least some embodiments of the present technology can be used with a variety of suitable fluids, such as water, aqueous solutions, hydrocarbons, glycols, and nitrogen. As such, although the term “waterjet” is used herein for ease of reference, unless the context clearly indicates otherwise, the term refers to a jet formed by any suitable fluid, and is not limited exclusively to water or aqueous solutions. The term “fluid,” as used herein, encompasses any suitable fluid phase depending on the context. Furthermore, the term “fluid,” as used herein, may be substituted in suitable instances with any of the narrower terms “aqueous fluid,” “water,” “liquid,” “aqueous liquid,” and “liquid water” to indicate common examples of suitable fluids in the context of waterjet processing. References herein to “ultrahigh pressures” refer to pressures suitable for high-volume waterjet processing of relatively hard materials. For example, the “ultrahigh pressures” described herein can be pressures greater than 30,000 psi, such as pressures within a range from 30,000 psi to 120,000 psi. It should be understood, however, that at least some features of the present technology can also be useful in the context of waterjet processing at lower pressures, such as pressures from 5,000 psi to 30,000 psi. Finally, unless the context clearly indicates otherwise, the terms “cutting,” “cut,” and the like refer to any suitable material modification caused by a waterjet, such as through cutting, piercing, shaping, carving, reaming, etching, milling, eroding, etc.

(17) FIG. 1 is a partially schematic and partially cross-sectional profile view of a waterjet system 100 in accordance with at least some embodiments of the present technology. As shown in FIG. 1, the waterjet system 100 can include a carriage 102 carrying a cutting head 104 via a kinematic chain 106. The cutting head 104 can be configured to direct a waterjet 108 toward a workpiece 110. The kinematic chain 106 can be configured to raise, lower, and tilt the cutting head 104 relative to the workpiece 110 while the cutting head 104 directs the waterjet 108 toward the workpiece 110. The waterjet system 100 can further include a motion assembly 112 configured to move the carriage 102 horizontally relative to the workpiece 110 while the cutting head 104 directs the waterjet 108 toward the workpiece 110. Below the carriage 102, the waterjet system 100 can include a catcher 114 containing a liquid reservoir 116 that dissipates the energy of the waterjet 108 after the waterjet 108 passes through the workpiece 110. The waterjet system 100 can also include slats 118 within the catcher 114 that support the workpiece 110. Ultrahigh pressure fluid lines, abrasive lines, and pneumatic lines associated with forming the waterjet 108 and operating the cutting head 104 are not shown in FIG. 1 to enhance clarity.

(18) The motion assembly 112 can include an x-axis subassembly 120 extending between two mounting towers 122 extending upwardly from the catcher 114. The motion assembly 112 can also include a y-axis subassembly 124 perpendicular to the x-axis subassembly 120. The x-axis subassembly 120 can include an x-axis actuator 126 within an x-axis bellow seal 128. Similarly, the y-axis subassembly 124 can include a y-axis actuator 130 within a y-axis bellow seal 132. The x-axis subassembly 120 and the y-axis subassembly 124 can also include internal tracks, joints, actuators, etc., which are not shown in FIG. 1 to enhance clarity. The cutting head 104 can be connected to the x-axis subassembly 120 via the y-axis subassembly 124 such that the x-axis subassembly 120 moves both the cutting head 104 and the y-axis subassembly 124. Together, the x-axis subassembly 120 and the y-axis subassembly 124 can move the cutting head 104 to any desired horizontal position within a rectangular field. In FIG. 1, the y-axis subassembly 124 is shown cantilevered off the x-axis subassembly 120. Alternatively, a counterpart of the y-axis subassembly 124 can be part of a bridge extending between two counterparts of the x-axis subassembly 120.

(19) With continued reference to FIG. 1, the waterjet system 100 can further include a user interface 134 and a controller 136. The user interface 134 can be configured to receive input from a user of the waterjet system 100 and to send data based on the input to the controller 136. The input can include, for example, one or more specifications (e.g., coordinates, geometries, dimensions, etc.) of a cutting project. The controller 136 can include a processor 138 and memory 140 and can be programmed with instructions (e.g., non-transitory instructions contained on a computer-readable medium) that, when executed, control operation of the waterjet system 100. The controller 136 can be operably connected to the user interface 134, to the motion assembly 112, and to the kinematic chain 106 via communication links 107. The communication links 107 can be separate or combined, and can have any suitable form. For example, the communication links 107 can include any suitable wired and/or wireless communication components, such as wires and transceivers (e.g., antennas, Wi-Fi access points, Bluetooth transceivers, nearfield communication devices, wireless modems, etc.). In some cases, the controller 136 is local. In other cases, the controller 136 is remote. Furthermore, communication between the controller 136 and other components of the waterjet system 100 can be direct or indirect (e.g., via the Internet and/or via an intermediate computing system).

(20) FIGS. 1 and 2 are profile views of the cutting head 104 and the kinematic chain 106 of the waterjet system 100. With reference to FIGS. 1-3 together, the cutting head 104 can include an elongate nozzle 142 and a waterjet outlet 144 at a distal end of the nozzle 142. The kinematic chain 106 can include a first joint 146, a second joint 148, and a third joint 150 rotatable about different respective axes. The first joint 146 can be in series between the cutting head 104 and the second joint 148. The second joint 148 can be in series between the first joint 146 and the third joint 150. The third joint 150 can be in series between the second joint 148 and the carriage 102. In at least some cases, the kinematic chain 106 also includes a fourth joint 152 in series between the third joint 150 and the carriage 102. The fourth joint 152 can be linearly adjustable to move the cutting head 104 vertically relative to the carriage 102.

(21) The first joint 146, the second joint 148, and the third joint 150 can be rotatably adjustable about a first axis 154 (illustrated as a line), a second axis 156 (also illustrated as a line), and a third axis 158 (illustrated as an “x”), respectively, within a first range of motion, a second range of motion, and a third range of motion, respectively. The second range of motion can be greater than the first range of motion. Furthermore, the third range of motion can be less than the first range of motion and less than the second range of motion. For example, the third range of motion can be less than or equal to 30 degrees (e.g., less than or equal to 60 degrees and/or less than or equal to 90 degrees), the first range of motion can be greater than 30 degrees and less than 360 degrees (e.g., greater than 60 degrees and less than 360 degrees), and the second range of motion can be greater than or equal to 360 degrees (e.g., +/−180 degrees, +/−360 degrees, +/−720 degrees, etc.). Each of the first joint 146, the second joint 148, and the third joint 150 can include a rotary actuator (not shown) configured to automatically execute movement instructions from the controller 136. The fourth joint 152 can include a linear actuator (also not shown) configured to automatically execute movement instructions from the controller 136.

(22) Rotatably adjusting the second joint 148 about the second axis 156 can change the position of the first axis 154. Similarly, rotatably adjusting the third joint 150 about the third axis 158 can change the respective positions of the first and second axes 154, 156. Rotatably adjusting the third joint 150 about the third axis 158 can also move the third joint 150 between a first state shown in FIG. 2 and a second state shown in FIG. 3. The second axis 156 can be vertical when the third joint 150 is in the first state and not vertical when the third joint 150 is in the second state. The second and third axes 156, 158 can have a fixed relationship, such as a fixed perpendicular relationship. Similarly, the first and second axes 154, 156 can have a fixed relationship, such as a fixed coplanar relationship with a fixed intervening angle (e.g., 30 degrees). In at least some cases, the third axis 158 is horizontal. Together, the first and second joints 146, 148 can cause the nozzle 142 to have a specified orientation relative to the workpiece 110 at a given time during a cutting project. Meanwhile, the motion assembly 112 and the fourth joint 152 can cause the nozzle 142 to have specified horizontal and vertical positions, respectively, relative to the workpiece 110. The nozzle 142 is shown coaxially aligned with the second axis 156 in FIGS. 2 and 3 to enhance clarity. During normal operation of the waterjet system 100, the nozzle 142 may or may not be aligned with the second axis 156 at any given time.

(23) Operating the third joint 150 is not necessary to achieve a full range of orientations of the nozzle 142. In other words, by operating only the first joint 146 and the second joint 148 the nozzle 142 can be oriented at any suitable angle relative to the workpiece 110 in a spherical sector defined by the range of motion of the first joint 146. It is understandable, then, that conventional waterjet systems configured to make angled cuts in workpieces do not include a counterpart of the third joint 150. These conventional waterjet systems can be characterized as two-axis systems. In contrast, the waterjet system 100 can be characterized as a three-axis system. Adding the third joint 150 adds cost and complexity to the waterjet system 100, but the inventors have discovered that the previously unrecognized benefits of the third joint 150 can outweigh this cost and complexity. Among these benefits is the potential to use the third joint 150 to move a kinematic singularity as needed to reduce or eliminate kinematic-singularity-related delay for a cutting project. This is particularly useful for cutting projects that call for tilting the nozzle 142 to reduce or eliminate taper in a product wall. As discussed above, the appropriate nozzle tilts for reducing or eliminating taper in a product wall typically change frequently within a small range in concert with changes in cutting speed. These conditions exacerbate kinematic-singularity-related delay when a kinematic singularity is within the small range. On the other hand, shifting the kinematic singularity by just a small angle can eliminate or nearly eliminate this problem.

(24) The third joint 150 can have one or more than one position during a single cutting project. For example, when the third joint 150 has a position that shifts a kinematic singularity so that the entire path the cutting head 104 is to follow to form a product does not cross or closely approach the kinematic singularity, maintaining the third joint 150 in that position throughout the cutting project may be appropriate. Alternatively, the third joint 150 may have different positions during different respective portions of a single cutting project when there is not a position of the third joint 150 suitable for reducing or eliminating kinematic-singularity-related delay at all portions of the cutting project. In at least the former case, it can be advantageous for the third joint 150 to be manually adjustable. In at least the latter case, it can be advantageous for the third joint 150 to be automatically adjustable. In FIGS. 1 and 2, the third joint 150 is shown as an automatically (not manually) adjustable joint. As discussed below with reference to FIGS. 4A-4B, in other cases, a counterpart of the third joint 150 can be manually adjustable. In these and still other cases, counterparts of the first and second joints 146, 148 can be automatically adjustable.

(25) FIGS. 4A and 5A are profile views of the cutting head 200 and a kinematic chain 202 of a waterjet system in accordance with at least some embodiments of the present technology. FIGS. 4B and 5B are enlarged views of portions of FIGS. 4A and 5A, respectively. With reference to FIGS. 4A-5B together, the kinematic chain 202 can include a third joint 204 that is manually adjustable to any one of three states. For example, the third joint 204 can include partially overlapping plates 206 with holes 208 that align from one plate 206 to the other plate 206 when the third joint 204 is in a given one of the three states. The third joint 204 can also include a pin 210 shaped to be inserted through an aligned pair of the holes 208 to hold the third joint 204 in a corresponding one of the states. In the illustrated case, the three states are a zero-degree angle, a four-degree angle, and an eight-degree angle. In FIGS. 4A and 4B, the pin 210 is inserted into the holes 208 corresponding to the zero-degree angle. In FIGS. 5A and 5B, the pin 210 is inserted into the holes 208 corresponding to the eight-degree angle. Whether manually adjustable or automatically adjustable, the third joint 204 and its counterparts can be step joints with a relatively small number of steps (e.g., at most 10 steps) rather than infinitely variable joints. This can be useful, for example, to reduce the complexity of the math used to control operation of the overall kinematic chain 202. In other cases, counterparts of the third joint 204 can be manually or automatically adjustable continuously rather than stepwise.

(26) FIGS. 6 and 7 are flow charts illustrating methods 300, 400, respectively, for operating a waterjet system in accordance with at least some embodiments of the present technology. The methods 300, 400 will be described with reference to features of the waterjet system 100 shown in FIGS. 1-3. It should be understood, however, that the methods 300, 400 and counterparts thereof are not limited to these features. As shown in FIG. 6, the method 300 can include operating the third joint 150 to rotate the cutting head 104, the first joint 146, and the second joint 148 about the third axis 158 relative to the workpiece 110 (block 302). For example, this can include moving the third joint 150 from a first state in which the second axis 156 is vertical to a second state in which the second axis 156 is not vertical. Alternatively or in addition, operating the third joint 150 can include moving the third joint 150 between two or more states in which the second axis 156 is off vertical by different respective angles. The movement of the third joint 150 can be stepwise or continuous, and can be automatic or manual. Next, the method 300 can include directing the waterjet 108 toward the workpiece 110 via the cutting head 104 (block 304). In some cases, moving the third joint 150 occurs only before directing the waterjet 108 toward the workpiece 110. In other cases, moving the third joint 150 occurs while directing the waterjet 108 toward the workpiece 110.

(27) The method 300 can further include moving (e.g., at varying speed) the carriage 102 horizontally relative to the workpiece 110 (block 306), operating the first joint 146 to rotate the cutting head 104 about the first axis 154 relative to the workpiece 110 (block 308), operating the second joint 148 to rotate the cutting head 104 and the first joint 146 about the second axis 156 relative to the workpiece 110 (block 310), and operating the fourth joint 152 to move the cutting head 104, the first joint 146, the second joint 148, and the third joint 150 vertically relative to the workpiece 110 (block 312). These operations can occur automatically in concert while directing the waterjet 108 toward the workpiece 110. Together, these operations can move the cutting head 104 along a path configured to form a product from the workpiece 110. The waterjet 108 can have different angles off vertical at different respective portions of the path. In at least some cases, the path includes adjustments in an angle by which the waterjet 108 is tilted relative to an adjacent wall of the product, thereby reducing or eliminating taper in the wall of the product, the taper being that associated with a non-cylindrical shape of the waterjet 108. When the speed at which the carriage 102 moves horizontally relative to the workpiece 110 varies, the adjustments in the angle by which the waterjet 108 is tilted relative to the adjacent wall of the product can at least partially compensate for an effect of the varying speed on the taper. Moving the third joint 150, which (as mentioned above) can occur before and/or while moving the cutting head 104 along the path, can shift a kinematic singularity away from the path.

(28) As shown in FIG. 7, the method 400 can include receiving a geometry of a product to be cut from the workpiece 110 (block 402). For example, the geometry can be vector model of the product. The method 400 can further include generating instructions for moving the cutting head 104 along a path relative to the workpiece 110 while the cutting head 104 directs the waterjet 108 toward the workpiece 110 to form the product. This can include generating instructions for operating the motion assembly 112 (block 404), generating instructions for operating the first joint 146 (block 406), generating instructions for operating the second joint 148 (block 408), and generating instructions for operating the third joint 150 (block 410). The instructions for operating the motion assembly 112 can include instructions for operating the motion assembly 112 to move the cutting head 104 horizontally at different respective speeds at different respective portions of the path. Correspondingly, the instructions for operating the first and second joints 146, 148 can include instructions for operating the first and second joints 146, 148 to at least partially compensate for an effect of the different horizontal speeds on taper in a wall of the product, the taper being that associated with a non-cylindrical shape of the waterjet 108. In these and other cases, the instructions for operating the first and second joints 146, 148 can include instructions for operating the first and second joints 146, 148 to reduce or eliminate the taper. The instructions for operating the third joint 150 can include instructions for operating the third joint 150 to shift a kinematic singularity away from the path.

(29) The method 400 can further include prompting a user of the waterjet system 100 to manually operate the third joint 150 to shift a kinematic singularity away from the path. For example, the controller 136 can calculate a suitable position for the third joint 150 to avoid kinematic singularities based on the complete instructions for a given cutting operation. A corresponding algorithm can include determining the angle between the nozzle axis and the second axis 156 at each increment during the cutting operation, calculating a minimum angle of the third joint 150 to prevent the angle between the nozzle axis and the second axis 156 from being zero at any increment, and then adding a buffer (e.g., 10 degrees) to the calculated minimum angle. The controller 136 can then determine a setting (e.g., a stepwise setting) for the suitable position of the third joint 150. The waterjet system 100 can then communicate this setting to a user of the waterjet system 100 via the user interface 134. After the user manually operates the third joint 150 in response to the communication, the method 400 can include automatically operating the first joint 146, the second joint 148, and the motion assembly 112 based at least partially on the instructions. Alternatively, the controller 136 can automatically operate the first joint 146, the second joint 148, the third joint 150, and the motion assembly 112 based at least partially on the instructions.

(30) The third joint 150 can have the same or different positions during the full duration of a cutting operation. Causing the third joint 150 to have different positions during the full duration of a cutting operation can be useful, for example, when the cutting operation involves forming walls at significantly different respective angles off vertical and compensating for taper. In these and other cases, no single position of the third joint 150 may be adequate to avoid kinematic singularities throughout the full duration of the cutting operation. Accordingly, the controller 136 can determine different suitable positions for the third joint 150 at different respective portions of the cutting operation. A corresponding algorithm can be the same as the algorithm described above for determining a single suitable position for the third joint 150, except performed on different subsets of all increments within the cutting operation. When the subsets are very small, control of the third joint 150 can be dynamic and in concert with operation of the first joint 146 and the second joint 148. Other control methods involving the third joint 148 are also possible.

(31) This disclosure is not intended to be exhaustive or to limit the present technology to the precise forms disclosed herein. Although specific embodiments are disclosed herein for illustrative purposes, various equivalent modifications are possible without deviating from the present technology, as those of ordinary skill in the relevant art will recognize. Accordingly, this disclosure and associated technology can encompass other embodiments not expressly shown or described herein. In some cases, well-known structures and functions have not been shown or described in detail to avoid unnecessarily obscuring the description of embodiments of the present technology. Although steps of methods may be presented herein in a particular order, in alternative embodiments, the steps may have another suitable order. Similarly, certain aspects of the present technology disclosed in the context of particular embodiments can be combined or eliminated in other embodiments. Furthermore, while advantages associated with certain embodiments may have been disclosed in the context of those embodiments, other embodiments can also exhibit such advantages, and not all embodiments need necessarily exhibit such advantages or other advantages disclosed herein to fall within the scope of the present technology.

(32) Certain aspects of the present technology may take the form of computer-executable instructions, including routines executed by a controller or other data processor. In some embodiments, a controller or other data processor is specifically programmed, configured, or constructed to perform one or more of these computer-executable instructions. Furthermore, some aspects of the present technology may take the form of data (e.g., non-transitory data) stored or distributed on computer-readable media, including magnetic or optically readable or removable computer discs as well as media distributed electronically over networks. Accordingly, data structures and transmissions of data particular to aspects of the present technology are encompassed within the scope of the present technology. The present technology also encompasses methods of both programming computer-readable media to perform particular steps and executing the steps.

(33) Throughout this disclosure, the singular terms “a,” “an,” and “the” include plural referents unless the context clearly indicates otherwise. Similarly, unless the word “or” is expressly limited to mean only a single item exclusive from the other items in reference to a list of two or more items, then the use of “or” in such a list is to be interpreted as including (a) any single item in the list, (b) all of the items in the list, or (c) any combination of the items in the list. Additionally, the terms “comprising” and the like are used throughout this disclosure to mean including at least the recited feature(s) such that any greater number of the same feature(s) and/or one or more additional types of features are not precluded. Directional terms, such as “upper,” “lower,” “front,” “back,” “vertical,” and “horizontal,” may be used herein to express and clarify the relationship between various elements. It should be understood that such terms do not denote absolute orientation. Reference herein to “one embodiment,” “an embodiment,” or similar formulations means that a particular feature, structure, operation, or characteristic described in connection with the embodiment can be included in at least one embodiment of the present technology. Thus, the appearances of such phrases or formulations herein are not necessarily all referring to the same embodiment. Furthermore, various particular features, structures, operations, or characteristics may be combined in any suitable manner in one or more embodiments.