Motion control method and system for bipolar coordinate 3D printer

Abstract

The invention discloses a bipolar coordinate 3D printer motion control method and system, and belongs to the technical field of additive manufacturing. In order to overcome the technical defects that an existing bipolar coordinate printer is complex in kinematics model and poor in calculation real-time performance, a swing arm rotation center O1 is fixedly arranged on an X axis (a, 0) or a Y axis (0, a) of a carrying table coordinate system, the length L of a swing arm is restrained to be equal to the distance a, and an optimization model based on the isosceles triangle geometrical relationship is established. On the basis of the geometric constraint, a deterministic closed-form solution for directly calculating a swing arm rotation angle phi and a carrying table rotation angle theta from model coordinates (x, y) is derived, and the iterative solution requirement in a traditional method is thoroughly eliminated. The system supports a precision controllable mechanism based on approximate calculation of a table look-up method, a CORDIC algorithm and the like, and multi-printing-head phase compensation cooperative scheduling. The real-time performance of calculation is remarkably improved while the printing precision is guaranteed, and the multi-material printing function is achieved.

Description

Technical Field

[0001] This invention relates to the field of additive manufacturing technology, specifically to a motion control method, system, and printer device for a 3D printer based on an optimized bipolar coordinate system. Background Technology

[0002] Current 3D printers primarily employ Cartesian or unipolar coordinate systems. Multipolar coordinate systems, as an emerging alternative, offer potential advantages such as simpler and more compact structures. Among publicly available patents, CN107738444A discloses a 3D printer using bipolar coordinates, which forms a cascaded bipolar coordinate system through a horizontally movable slider and a rotatable print head. This approach has significant drawbacks: its kinematic model relies on a complex system of two nonlinear equations (X=(a*cosA)(b*cosB), Y=a*sinA+b*sinB), requiring extensive computation and involving multiple solutions or iterative iterations, making it difficult to meet real-time requirements in high-speed printing scenarios. CN110341190B and CN120134616A disclose 3D printer structures based on multipolar coordinates, but neither discloses the specific motion control algorithms. Furthermore, none of the aforementioned patent solutions address features such as multi-print head integration and adaptive precision control. Therefore, existing multi-polar coordinate printers still suffer from technical bottlenecks such as complex motion control algorithms, poor real-time performance, and limited functionality, which restricts their practical application in high-speed, high-precision, and multi-material printing fields. This application is an improvement on the prior application CN120134616A, and specifically innovates its undisclosed control algorithm. Summary of the Invention

[0003] The purpose of this invention is to overcome the shortcomings of existing bipolar coordinate 3D printer motion control algorithms, such as complexity, poor real-time performance, and insufficient functional scalability, and to provide a motion control method and system that is computationally efficient, has good real-time performance, and supports multi-functional integration.

[0004] To achieve the above objectives, the core concept of this invention is as follows: by optimizing the rotation center (sliding sleeve axis) O1 of the swing arm to a fixed position (a,0) or (0, a) on the X or Y axis of the platform coordinate system, and constraining L=a, a simplified model based on the geometric relationship of isosceles triangles is established, and a direct calculation formula is derived according to the triangle cosine theorem, thereby replacing the iterative solution of traditional complex equation systems.

[0005] To achieve the above objectives, the present invention provides a motion control method for a bipolar coordinate 3D printer, characterized in that the bipolar coordinate 3D printer includes a fixedly disposed sliding sleeve axis (O1), a stage rotatable about the stage center (O), and a swing arm with one end rotatably connected to the sliding sleeve axis (O1) and the other end provided with a print head; wherein the sliding sleeve axis (O1) is located at (a, 0) or (0, a), and the length L of the swing arm (the distance from the extrusion port of the print head to the sliding sleeve axis) is equal to the distance a from the sliding sleeve axis to the center of the stage; the method includes the following steps: S1: Obtain the coordinates (x, y) of the target printing point P in the model coordinate system, wherein the model coordinate system is fixed to the platform and its origin coincides with the center of the platform; S2: Calculate the polar coordinate parameters of the target printing point, including: Polar diameter: ; Polar angle: θ0 = atan2(y, x); S3: Based on the position of the sliding sleeve axis in the fixed coordinate system, select the corresponding preset calculation formula to solve the swing arm rotation angle φ and the stage rotation angle θ required for the print head to reach the target printing point. The preset calculation formula is determined by trigonometric geometric relations based on the geometric constraint of L=a, and the swing arm rotation angle φ is constrained within the interval [0,π]. S4: Drive the stage to rotate by the stage rotation angle θ, and simultaneously drive the swing arm to rotate around the axis of the sliding sleeve by the swing arm rotation angle φ, so that the print head moves to the target printing point P.

[0006] Further, in step S3, when the sliding sleeve axis O1 is located at (a, 0), the swing arm rotation angle φ is the angle between the swing arm and the positive X-axis direction, and the preset calculation formula includes: Calculate the auxiliary angle β, where β = arccos(ρ / (2a)); The rotation angle of the swing arm is determined to be φ = 2β; The rotation angle of the stage is determined to be θ = β - θ0.

[0007] Further, in step S3, when the sliding sleeve axis O1 is located at (0, a), the swing arm rotation angle φ is the angle between the swing arm and the negative Y-axis direction, and the preset calculation formula includes: Determine the swing arm rotation angle φ = arccos(1 - ρ) 2 / (2a 2 )); The rotation angle of the platform is determined to be θ = φ / 2 - θ0.

[0008] Optionally, in step S3, the calculation of the inverse cosine function arccosine is implemented using an approximate calculation method, such as a lookup table method, a polynomial approximation method, or the CORDIC algorithm. For the lookup table method, a lookup table containing 256 uniformly discrete entries is preferred, combined with a linear interpolation algorithm, which can achieve a maximum angle calculation error of less than 0.01 radians on a typical microcontroller, meeting the real-time control requirements of high-speed printing. For the CORDIC algorithm, sufficient accuracy can be achieved without a hardware multiplier through 16 iterations.

[0009] Furthermore, it also includes step S5: controlling the print head to move in the vertical direction according to the Z coordinate of the target printing point P.

[0010] The present invention also provides a bipolar coordinate 3D printer motion control system for implementing the aforementioned printer motion control method, characterized in that it includes: The coordinate system configuration module is used to establish and maintain the fixed coordinate system; The trajectory generation module is used to generate a sequence of target point coordinates. The inverse kinematics solution module is configured to calculate the swing arm rotation angle φ and the platform rotation angle θ based on the calculation formula described under the conditions L=a and O1(a, 0) or O1(0, a) from the target point coordinates. The coordinated motion control module is used to drive the actuator according to φ and θ.

[0011] The present invention further provides a bipolar coordinate 3D printer, characterized in that it includes the aforementioned motion control system; its mechanical structure is configured such that: the swing arm rotates around a fixedly set sliding sleeve axis (O1), and the fixedly set sliding sleeve axis (O1) is located in the positive direction of the X-axis or Y-axis of the stage center (O), at a distance of a, and the swing arm length is equal to a.

[0012] Furthermore, it also includes a Z-axis relative motion mechanism for realizing the relative movement between the print head and the print stage in the Z-axis direction, and the Z-axis relative motion mechanism is linked with the cooperative motion control module.

[0013] Optionally, the swing arm is a disc-shaped structure, forming a turntable; at least two printheads are arranged circumferentially on the outer periphery of the turntable, and the distance from the extrusion port of each printhead to the rotation center of the turntable is a, and they have fixed installation phase angles δ1, δ2, δ3....

[0014] Optionally, the motion control system further includes: The printhead selection and scheduling module is used to dynamically select the active printhead from the plurality of printheads according to the needs of the current printing task; The phase compensation module is used to compensate the first rotation angle θ calculated by the inverse kinematics calculation module based on the fixed installation phase angle δ of the selected print head, so as to obtain the actual command angle θ'=θ-δ that drives the turntable to rotate, and to correct the phase offset at the start of printing.

[0015] Compared to the closest existing technology, this invention has achieved significant progress in many aspects: 1. Highly efficient and real-time motion control computation. This invention simplifies the model into a series of sequentially executed direct calculation formulas through geometric optimization, completely eliminating iteration and complex condition judgments. This enables the control system to achieve a stable control cycle even under high-speed printing, fundamentally solving the fundamental problem of poor real-time performance in existing bipolar printers due to algorithm complexity. It can be directly used for embedded controller implementation. 2. High control precision and motion consistency. The inverse kinematics calculation model of this invention has a definite and unique calculation path, which guarantees the consistency of motion commands from the algorithm principle. It can be combined with closed-loop real-time correction to effectively improve printing quality. 3. The high degree of coordination between the mechanical structure and kinematic model provides a physical basis for multifunctional integration. This invention integrates the moving parts into a swing arm (or turntable) that rotates around a fixed center, resulting in a more compact structure. This bipolar coordinate structure naturally supports the integration of multiple printheads circumferentially on the rotating parts (a structural extension improvement), and unified control is achieved through a phase compensation algorithm, which is either impossible to implement directly or inefficient in existing technology architectures. 4. Wide range of system functions. The standard and approximate calculation algorithms and multi-printhead collaborative scheduling algorithms proposed in this invention enable the printer to achieve an optimal balance between accuracy and efficiency, and to efficiently complete multi-material printing tasks, which can be extended to industrial-grade application scenarios. Attached Figure Description

[0016] Figure 1 This is a schematic diagram of the geometric relationship of the bipolar coordinate system described in this invention with the sliding sleeve axis located at (a,0).

[0017] Figure 2 This is a schematic diagram of the geometric relationship of the bipolar coordinate system described in this invention with the sliding sleeve axis located at (0,a).

[0018] Figure 3 This is an overall flowchart of the motion control method of the present invention.

[0019] Figure 4 This is a schematic diagram of the structure and multiple printhead positions of a multi-material printer according to an embodiment of the present invention.

[0020] Figure 5 This is a block diagram of the motion control system architecture of the present invention. Detailed Implementation

[0021] The present invention will be further described below with reference to the accompanying drawings and embodiments.

[0022] Example 1: Bipolar Coordinate System Establishment and Core Algorithm like Figure 1 , Figure 2 The diagram shows the geometric relationship of the bipolar coordinate system established in this invention. Mechanical initialization requires ensuring that the arm length L is equal to the distance a between the two rotation centers. A coordinate system is established with the platform center O as the origin (0,0) and the arm rotation center O1 fixed at (0,a) or (a, 0). The target point P(x,y) in this coordinate system is first calculated based on the polar coordinates of its polar radius. The polar angle θ0 = atan2(y, x) is then used to directly calculate the bipolar coordinate arm rotation angle φ and the platform rotation angle θ.

[0023] For the pivot point O1 of the swing arm fixed at (0, a), as follows Figure 1 The preset calculation formula is: Auxiliary angle β, where β = arccos(ρ / (2a)); The swing arm rotation angle φ = 2β; The platform rotation angle θ = β - θ0.

[0024] For boundary condition handling: When ρ=0 (target point is at the origin), theoretically there are infinitely many solutions. In this embodiment, θ=0 and φ=π are specified to ensure that the print head approaches the center from a fixed direction; when ρ=2a (target point is at the farthest end (2a,0)), θ=atan2(y,x)-π / 2 and φ=0; when 0<ρ<2a, the above formula is used for calculation. Through continuous processing, the movement of the stage and the swing arm is ensured to be smooth and without abrupt changes.

[0025] For the pivot point O1 of the swing arm fixed at (a, 0), as follows: Figure 2 The preset calculation formula is: Swing arm rotation angle φ=arccos(1-ρ 2 / (2a 2 )); The rotation angle of the platform is θ = φ / 2 - θ0.

[0026] Boundary condition handling: When ρ=0, let θ=0 and φ=0; when ρ=2a (the target point is located at (0,2a)), let θ=atan2(y,x)-π / 2 and φ=π.

[0027] To ensure that each reachable point corresponds to a unique joint angle solution, the above preset calculation formula constrains φ∈[0, π] to avoid multiple solution selection problems and simplify path planning; at the same time, it restricts the swing arm from rotating a full circle to avoid the feeding conduit and wires connecting the extruder head from getting tangled and excessively twisted, thus ensuring the stability and reliability of long-term material supply.

[0028] To achieve stable and continuous control of the system, it is necessary to handle boundary conditions, angle continuity, and abnormal situations during the actual motion control process. These are conventional technical means used by those skilled in the art.

[0029] Example 2: Approximate Calculation Implementation Method for the Inverse Cosine Function In practical embedded control systems, to meet real-time requirements, the inverse cosine function arccosine involved in the computation steps can be rapidly implemented using various approximation methods known in the art. These are all conventional technical choices for those skilled in the art. Specifically, they include, but are not limited to: (1) Table lookup method: The discrete function value table of arccos(x) in the domain is pre-calculated and stored. During runtime, the table is looked up according to the input value x, and an approximate result is obtained through algorithms such as linear interpolation. This method has an extremely fast calculation speed and is a common means to meet the requirements of real-time control; (2) Polynomial or rational function approximation method: This method uses polynomials or rational fractions to approximate the arccos(x) function within a specific interval. The coefficients can be determined through optimization methods such as the least squares method, which reduces the amount of computation while ensuring accuracy. (3) CORDIC iterative algorithm: It uses 16 iterations to approximate the arccos function value through simple shift and addition operations. No hardware multiplier is required, and it is suitable for FPGA or low-cost MCU implementation. (4) Hybrid method: Combining the above methods, such as using a segmented strategy, using different precision table lookup or polynomial approximation in different intervals.

[0030] Those skilled in the art will understand that the choice of approximation method requires a conventional trade-off between computational accuracy, speed, memory usage, and processor capability. For this invention, any of the methods described above can achieve the invention's objective. As a specific embodiment, when the maximum angle calculation error is required to be less than 0.01 radians, a lookup table containing 256 entries, combined with linear interpolation, can meet the real-time control requirements for high-speed printing on a typical ARM Cortex-M series microcontroller.

[0031] Example 3: Implementation of Motion Control Method The overall flowchart of the motion control method of this invention is as follows: Figure 3As shown, taking the configuration where the sliding sleeve axis is located at (0, a) as an example, the main steps of motion control for a bipolar coordinate printer are as follows: Step S1: Coordinate Acquisition. Obtain the coordinates (x, y, z) of the target printing point P in the model coordinate system. These coordinates come from the slice data of the 3D model, where (x, y) are the horizontal coordinates and z is the vertical height; Step S2: Polar coordinate calculation. The calculation formula is: θ0 = atan2(y, x); Step S3: Inverse kinematics calculation. First, check reachability: if ρ > 2a, the point is unreachable and anomaly handling is performed; if ρ ≤ 2a, then: β = arccos(ρ / (2a)), φ = 2β, θ = β - θ0 In practical embedded systems, Arccos calculations can be performed using approximation methods. For example, using a 256-point lookup table combined with linear interpolation can significantly improve calculation speed while ensuring sufficient accuracy. Step S4: Motion Execution. The calculated (θ, φ) is converted into motor control signals to drive the stage to rotate by an angle θ and the swing arm to rotate by an angle φ. During this process, Step S5 is executed synchronously: the vertical movement of the print head is controlled according to the layer height in the z-coordinate, and synchronized with the planar movement through the Z-axis relative motion mechanism to ensure a constant extrusion height.

[0032] For the configuration where the sleeve shaft center is located at (a,0), steps S1, S2, and S4 in the motion control process are the same as those for the configuration where the sleeve shaft center is located at (0,a). The inverse kinematics calculation in step S3 is performed according to the preset calculation formula and related algorithm corresponding to Example 1.

[0033] Example 4: Structure and Collaborative Control Method of Rotary Multi-Material Bipolar Coordinate Printer A schematic diagram of the mechanical structure of a rotary multi-material bipolar coordinate printer is shown below. Figure 4 (a) mainly includes a rotatable printing stage 200, a Z-axis motion mechanism 300, a swing arm 400 and multiple print heads 401. The printing stage 200 is used to drive the stage to rotate by an angle θ and to receive printing material. The Z-axis motion mechanism 300 is used to drive the relative movement between the print head and the printing stage 200 in the Z-axis direction. The swing arm 400 is used to drive the print head 401 to swing around the rotation center O1.

[0034] Arm swing Figure 4(b) Specifically, a rigid turntable 400 is implemented, with its rotation center coinciding with O1. Multiple printheads (401a, 401b, 401c…) are evenly installed on the outer periphery of the turntable 400. The distance from the extrusion port of each printhead to the center is 'a', and each printhead has a fixed installation phase angle (δ1, δ2, δ3…). The turntable 400 is configured to be rotated by a synchronous belt and the printhead Z-axis shifting mechanism is configured via a motor drive mechanism 410. Mechanical interference can be completely avoided when the printhead is not working.

[0035] The main steps for coordinated control among multiple printheads are as follows: 1. Dynamically select the active printhead i (i=1, 2, 3..., corresponding to printheads 401a, 401b, 401c...) based on the material properties in the slice file; 2. After selecting and activating printhead i, compensate for the calculated reference swing arm angle θ. The command angle for the actual drive stage rotation angle is: θ'=θ-δ i Where δ i This is the installation phase angle of printhead i relative to the reference position. This angle is determined by the calibration program during mechanical assembly and stored in the system parameters.

[0036] This mechanism enables multiple printheads to work efficiently and without interference within a unified kinematic framework, achieving complex multi-material printing.

[0037] Example 5: Motion Control System Architecture like Figure 5 As shown, the motion control system 100 of the present invention consists of four main modules: a coordinate system configuration module 110, a trajectory generation module 120, an inverse kinematics calculation module 130, and a cooperative motion control module 140. The main functions of each module include: The coordinate system configuration module 110 is used to establish and maintain the aforementioned fixed coordinate system, including origin calibration and storage of geometric parameter a; Trajectory generation module 120 is used to generate a sequence of target point coordinates; The inverse kinematics solution module 130 is configured to use the aforementioned preset calculation formula based on the conditions L=a and O1(a, 0) or O1(0, a) to calculate the swing arm rotation angle φ, the platform rotation angle θ, and the floor height Z from the target point coordinates, and to process the boundary conditions. The coordinated motion control module 140 is used to drive the actuator according to φ, θ and Z.

[0038] For bipolar printers with multiple printheads, the motion control system also includes: The printhead selection and scheduling module 150 is used to dynamically select the active printhead from multiple printheads according to the needs of the current printing task. The phase compensation module 160 is used to compensate the first rotation angle θ calculated by the inverse kinematics calculation module based on the fixed installation phase angle δ of the print head, so as to obtain the actual command angle θ'=θ-δ that drives the turntable to rotate.

[0039] The control system module can be fully integrated into existing 3D printer open-source firmware (such as Marlin, Klipper) or commercial control systems, and those skilled in the art can implement it in software based on the above principles.

[0040] It should be noted that the calculation formulas given for the two different configurations of the sliding sleeve shaft center located at (a, 0) and (0, a) are mathematically unified. The inverse kinematics formulas for both configurations can be uniformly expressed as "solving by using an auxiliary angle determined by ρ and a (the specific expression of which varies depending on the configuration) in the form of 'φ=2×auxiliary angle' and 'θ=auxiliary angle-θ0'". The different expressions given in the claims are the simplest and most direct manifestations of the above-mentioned unified principle for their respective geometric configurations. In practical applications, the sliding sleeve shaft center O1 may not be limited to being located at (a, 0) or (0, a), but may also be located in other quadrants, such as (-a, 0) or (0, -a). The constraint range of the swing arm rotation angle φ can also be φ∈[π:2π]. These configurations based on the above two basic cases through coordinate rotation transformation should all be covered within the protection scope of this invention.

[0041] The above description, in conjunction with specific preferred embodiments, provides a further detailed explanation of the present invention. It should not be construed that the specific implementation of the present invention is limited to these descriptions. For those skilled in the art, various simple deductions or substitutions can be made without departing from the concept of the present invention, and all such modifications and substitutions should be considered within the scope of protection of the present invention.

Claims

1. A motion control method for a bipolar coordinate 3D printer, characterized in that, The bipolar coordinate 3D printer includes a fixed sliding sleeve axis (O1), a stage that can rotate around the stage center (O), and a swing arm with one end rotatably connected to the sliding sleeve axis (O1) and the other end equipped with a print head; wherein, the sliding sleeve axis (O1) is located at (a, 0) or (0, a), and the length L of the swing arm is equal to the distance a from the sliding sleeve axis to the stage center; The method includes the following steps: S1: Obtain the coordinates (x, y) of the target printing point P in the model coordinate system, wherein the model coordinate system is fixed to the platform and its origin coincides with the center of the platform; S2: Calculate the polar coordinate parameters of the target printing point, including the polar radius. And the polar angle θ0 = atan2(y,x); S3: Based on the position of the sliding sleeve axis in the fixed coordinate system, select the corresponding preset calculation formula to solve the swing arm rotation angle φ and the stage rotation angle θ required for the print head to reach the target printing point. The preset calculation formula is determined by trigonometric geometric relations based on the geometric constraint of L=a, and the swing arm rotation angle φ is constrained in the interval [0,π] to prevent the swing arm from rotating a full circle. S4: Drive the stage to rotate by the stage rotation angle θ, and simultaneously drive the swing arm to rotate around the axis of the sliding sleeve by the swing arm rotation angle φ, so that the print head moves to the target printing point P.

2. The motion control method according to claim 1, characterized in that, In step S3, when the sliding sleeve axis O1 is located at (a, 0), the swing arm rotation angle φ is the angle between the swing arm and the positive X-axis direction, and the preset calculation formula includes: Calculate the auxiliary angle β, where β = arccos(ρ / (2a)); The rotation angle of the swing arm is determined to be φ = 2β; The stage rotation angle is determined to be θ = β - θ0; When ρ=0, let θ=0 and φ=π; when ρ=2a, let θ=atan2(y,x)-π / 2 and φ=0 to ensure the continuity of the angle.

3. The motion control method according to claim 1, characterized in that, In step S3, when the sliding sleeve axis O1 is located at (0, a), the swing arm rotation angle φ is the angle between the swing arm and the negative Y-axis direction, and the preset calculation formula includes: Determine the swing arm rotation angle φ = arccos(1 - ρ) 2 / (2a 2 )); The rotation angle of the stage is determined to be θ = φ / 2 - θ0; When ρ=0, let θ=0 and φ=0; when ρ=2a, let θ=atan2(y,x)-π / 2 and φ=π to ensure the continuity of the angle.

4. The motion control method according to claim 2 or 3, characterized in that, In step S3, the calculation of the arccosine function arccos is implemented using an approximate calculation method, and the calculation error of the approximate calculation method is configured to meet the preset printing accuracy requirements of the printer.

5. The motion control method according to claim 1, characterized in that, It also includes step S5: controlling the print head to move in the vertical direction according to the Z coordinate of the target print point P.

6. A motion control system for a bipolar coordinate 3D printer, used to implement the method as described in any one of claims 1-5, characterized in that, include: The coordinate system configuration module is used to establish and maintain the fixed coordinate system; The trajectory generation module is used to generate a sequence of target point coordinates. The inverse kinematics solution module is configured to use the calculation formula based on the conditions L=a and O1(a, 0) or O1(0, a), and to use the calculation formula described in claim 2 or 3 to calculate the swing arm rotation angle φ and the platform rotation angle θ from the target point coordinates. The coordinated motion control module is used to drive the actuator according to φ and θ.

7. A bipolar coordinate 3D printer, characterized in that, The motion control system as described in claim 6 is configured such that the swing arm rotates around a fixed sliding sleeve axis (O1), and the fixed sliding sleeve axis (O1) is located in the positive direction of the X-axis or Y-axis of the platform center (O) at a distance of a, and the length of the swing arm is equal to a.

8. The bipolar coordinate 3D printer according to claim 7, characterized in that, It also includes a Z-axis relative motion mechanism for realizing the relative motion between the print head and the print stage in the Z-axis direction.

9. The bipolar coordinate 3D printer according to claim 7, characterized in that, The swing arm has a disc-shaped structure, forming a turntable; at least two printheads are arranged circumferentially on the outer periphery of the turntable, and the distance from the extrusion port of each printhead to the rotation center of the turntable is 'a', and each printhead has a preset installation phase angle δ. i .

10. The bipolar coordinate 3D printer according to claim 7, characterized in that, The motion control system further includes: The printhead selection and scheduling module is used to dynamically select the active printhead from the plurality of printheads according to the needs of the current printing task; The phase compensation module is used to adjust the fixed installation phase angle δ of the selected printhead. i The first rotation angle θ calculated by the inverse kinematics solution module is compensated to obtain the actual command angle θ' = θ - δ that drives the turntable to rotate. i And according to the phase angle δ i The calibration value is used to correct the starting position of the print.

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