A five-axis support-free continuous light solidification molding method and system

Abstract

This invention proposes a five-axis unsupported continuous photopolymerization molding method and system. The method includes: acquiring surface geometric feature data based on the three-dimensional data of the model to be printed; acquiring kinematic chain definition parameters and generating a topology type identifier based on a predefined topology structure of the equipment's mechanical layout; acquiring the resin viscosity value and matching the optimal layer thickness, feed rate, equivalent cone angle, density, and surface tension coefficient from a preset parameter table; using the surface geometric feature data, topology type identifier, and matched process parameters, generating a dynamic posture sequence and a continuous spatial motion trajectory through kinematic joint optimization; and driving the first and second kinematic chains based on the posture sequence and trajectory to complete the five-axis unsupported continuous photopolymerization molding. This invention eliminates edge damage caused by support structures, improves molding accuracy and surface quality, avoids curing interference caused by discrete layer peeling, and achieves continuous and uniform photopolymerization molding.

Description

Technical Field

[0001] This invention relates to the field of additive manufacturing technology, and in particular to a five-axis unsupported continuous photopolymerization molding method and system. Background Technology

[0002] Current photopolymer 3D printing (SLA, DLP, or LCD) mostly employs a discrete layering process of "exposure-peeling-lifting". To prevent overhanging or undercut structures from collapsing during peeling, stress must be transferred by a support structure. However, support contact points are prone to damaging delicate edges (such as dental shoulders or optical interfaces), resulting in significantly increased surface roughness after removal and requiring extensive post-processing. Furthermore, support shielding and oxygen suppression can lead to uneven local curing, residual fluctuations in extractable monomers, and affect biocompatibility and long-term stability.

[0003] Existing five-axis photopolymerization equipment mostly adopts the "tilted trough" or "static layering + rotational fine-tuning" scheme, which still does not break away from the layer-by-layer peeling logic and cannot fundamentally eliminate support generation. At the same time, traditional slicing algorithms separate attitude planning and trajectory generation, making it difficult to achieve continuous spreading and uniform curing under five-degree-of-freedom kinematic coupling.

[0004] Furthermore, while the few currently available continuous photopolymerization technologies (such as the CLIP process based on an oxygen-inhibiting layer) can achieve uninterrupted curing on planar or near-planar surfaces, their limitations in resin self-spreading ability and window permeability make them difficult to extend to arbitrary freeform surface molding scenarios. Simultaneously, truly "unsupported" molding requires the system to dynamically balance gravity, surface tension, curing rate, and motion acceleration in real time on any oriented, overhanging, concave, or highly curved surface; otherwise, resin sagging, uneven thickness, or discontinuous curing can easily occur. In existing solutions, even with equipment equipped with multi-axis turntables, trajectory generation still relies on discrete contour points output by traditional layer-slicing software, which are then converted into motion control code after post-processing. This results in discontinuous rotation angles and abrupt acceleration changes in the posture sequence, leading to localized excessive accumulation or failed curing layer peeling. Therefore, how to achieve five-axis continuous trajectory optimization driven by surface geometry features and directly embed the physical constraints of resin spreading into kinematic joint planning has become a key technical challenge urgently needing to be solved in this field. Summary of the Invention

[0005] In view of the above, the main objective of this invention is to propose a five-axis unsupported continuous photopolymerization molding method to solve the above-mentioned technical problems.

[0006] This invention proposes a five-axis unsupported continuous photopolymerization molding method, the method comprising the following steps: Step 1: Obtain surface geometric feature data based on the 3D data of the model to be printed; Step 2: Based on the mechanical layout of the equipment, a predefined topology is used to obtain the kinematic chain definition parameters and generate a topology type identifier. Step 3: Obtain the resin viscosity value, and based on the resin viscosity value, match the optimal layer thickness, optimal feed speed, optimal equivalent cone angle, resin density, and resin surface tension coefficient from the preset parameter table. Step 4: Using surface geometric feature data, topology type identifier, kinematic chain definition parameters, optimal layer thickness, optimal feed rate, optimal equivalent cone angle, resin density, and resin surface tension coefficient, a dynamic equilibrium relationship between the surface to be cured and the resin coating is constructed. Based on the dynamic equilibrium relationship between the surface to be cured and the resin coating, combined with the included angle constraint, a dynamic posture sequence and a continuous spatial motion trajectory are generated through kinematic joint optimization. Step 5: Based on the dynamic posture sequence and continuous spatial motion trajectory, drive the first kinematic chain and the second kinematic chain to complete the five-axis unsupported continuous photopolymerization molding.

[0007] This invention also proposes a five-axis unsupported continuous photopolymerization molding system, the system comprising: The feature data acquisition module is used for: Obtain surface geometric feature data based on the 3D data of the model to be printed; The topology type identifier generation module is used for: Based on the mechanical layout of the device, a predefined topology is used to obtain the kinematic chain definition parameters and generate a topology type identifier. The parameter acquisition module is used for: Obtain the resin viscosity value, and based on the resin viscosity value, match the optimal layer thickness, optimal feed rate, optimal equivalent cone angle, resin density, and resin surface tension coefficient from the preset parameter table; The kinematic joint optimization module is used for: By utilizing surface geometric feature data, topology type identifiers, kinematic chain definition parameters, optimal layer thickness, optimal feed rate, optimal equivalent cone angle, resin density, and resin surface tension coefficient, a dynamic equilibrium relationship between the surface to be cured and the resin coating is constructed. Based on the dynamic equilibrium relationship between the surface to be cured and the resin coating, combined with angular constraints, dynamic posture sequences and continuous spatial motion trajectories are generated through kinematic joint optimization. Curing module, used for: Based on dynamic posture sequences and continuous spatial motion trajectories, the first and second motion chains are driven to complete five-axis unsupported continuous photopolymerization molding.

[0008] Compared with the prior art, the beneficial effects of the present invention are as follows: 1. This invention achieves unsupported continuous photopolymerization molding by generating dynamic posture sequences and continuous spatial motion trajectories through five-axis linkage kinematic joint optimization. This completely eliminates the edge damage problem caused by support structures in traditional processes, significantly improving the edge accuracy of the molded parts.

[0009] 2. This invention is based on matching the resin viscosity to the optimal process parameters and combining dynamic equilibrium relationship for attitude verification, which ensures the self-adhesion and uniform curing of the resin under the action of gravity and surface tension, and does not require additional polishing treatment to improve surface quality.

[0010] 3. This invention drives the motion chain through continuous spatial motion trajectory, abandoning the traditional discrete layering logic of "exposure-peeling-lifting" and avoiding the interference of support occlusion on photocuring. Attached Figure Description

[0011] Figure 1 This is a flowchart of the five-axis unsupported continuous photopolymerization molding method proposed in this invention; Figure 2 This is a schematic diagram of the framework of the five-axis unsupported continuous photopolymerization molding system proposed in this invention. Detailed Implementation

[0012] Embodiments of the present invention are described in detail below. Examples of these embodiments are shown in the accompanying drawings, wherein the same or similar reference numerals denote the same or similar elements or elements having the same or similar functions throughout. The embodiments described below with reference to the accompanying drawings are exemplary and are only used to explain the present invention, and should not be construed as limiting the present invention.

[0013] These and other aspects of the embodiments of the present invention will become clear from the following description and accompanying drawings. In these descriptions and drawings, some specific embodiments of the present invention are specifically disclosed to illustrate some ways of implementing the principles of the embodiments of the present invention; however, it should be understood that the scope of the embodiments of the present invention is not limited thereto.

[0014] Please see Figure 1 This invention proposes a five-axis unsupported continuous photopolymerization molding method, which includes the following steps: Step 1: Obtain surface geometric feature data based on the 3D data of the model to be printed.

[0015] Specifically, this invention uses an oral scanner to obtain digital impressions of the patient's teeth, and imports the dental crown model into the printing control system in STL format. The system extracts surface geometric feature data from the three-dimensional data, including information such as the shoulder curve, occlusal surface curvature distribution, and axial surface morphology of the crown model.

[0016] Step 2: Based on the mechanical layout of the equipment, a predefined topology is used to obtain the kinematic chain definition parameters and generate a topology type identifier. In step 2, based on the mechanical layout of the equipment and a predefined topology, the kinematic chain definition parameters are obtained through the predefined topology, and a topology type identifier is generated. This topology type identifier is divided into three types: standard topology, first variant topology, and second variant topology. The standard topology is defined as follows: the first kinematic chain is a linear module, and the second kinematic chain is a composite rotary platform. The first variant topology is defined as follows: the first kinematic chain is a coating head with rotational degrees of freedom, and the second kinematic chain is a fixed or translational platform. The second variant topology is defined as a five-axis drive configuration with redundant rotational degrees of freedom; wherein the first kinematic chain is used to control the spatial movement of the coating or curing structure, and the second kinematic chain is used to control the pose adjustment of the workpiece platform.

[0017] It should be noted that the "five-axis" mentioned in this invention refers to the minimum number of degrees of freedom required to achieve unsupported continuous photopolymerization molding. The five-axis drive configuration with redundant rotational degrees of freedom described in the second variant topology is an extended configuration based on the five-axis configuration. The additional redundant rotational degrees of freedom are used to avoid mechanical limitations and improve motion smoothness. The actual molding process is still based on five-degree-of-freedom kinematic constraints. Therefore, the "five-axis" of this invention covers all topological variants, including redundant degrees of freedom.

[0018] Step 3: Obtain the resin viscosity value, and based on the resin viscosity value, match the optimal layer thickness, optimal feed speed, optimal equivalent cone angle, resin density, and resin surface tension coefficient from the preset parameter table. Specifically, please refer to Table 1. This invention is adapted to compliant dental photosensitive resins of different viscosities and provides an operable parameter matching window based on process calibration.

[0019] Table 1. Material Compatibility Parameter Window

[0020] Among them, from the resin viscosity value Matching the optimal equivalent cone angle The specific rules are as follows: when hour, ; when hour, ; when hour, .

[0021] The equivalent cone angle is a process characteristic angle determined by the resin viscosity, characterizing the maximum tilt angle at which the resin can resist gravity sagging during the motion coating process. This angle is experimentally calibrated to a constant (e.g., 5°~15° given in the table). This equivalent cone angle is used to characterize the resin's ability to resist gravity sagging in the dynamic equilibrium relationship. The larger the equivalent cone angle, the more the resin can withstand a larger surface tilt angle without sagging under given coating conditions. Therefore, a smaller layer thickness and a lower feed rate are required to ensure that the dynamic equilibrium relationship is valid.

[0022] Step 4: Using surface geometric feature data, topology type identifier, kinematic chain definition parameters, optimal layer thickness, optimal feed rate, optimal equivalent cone angle, resin density, and resin surface tension coefficient, a dynamic equilibrium relationship between the surface to be cured and the resin coating is constructed. Based on the dynamic equilibrium relationship between the surface to be cured and the resin coating, combined with the included angle constraint, a dynamic posture sequence and a continuous spatial motion trajectory are generated through kinematic joint optimization. In step 4, the dynamic equilibrium relationship between the surface to be cured and the resin coating is constructed using surface geometric feature data, topology type identifier, kinematic chain definition parameters, optimal layer thickness, optimal feed rate, optimal equivalent cone angle, resin density, and resin surface tension coefficient. Based on this dynamic equilibrium relationship, and combined with angular constraints, a dynamic attitude sequence and continuous spatial motion trajectory are generated through kinematic joint optimization. The specific steps are as follows: Step 401: Obtain the current forming progress, and determine the optimal orientation parameters of the workpiece platform based on the surface geometric feature data and the current forming progress; Step 402: Using the optimal orientation parameters of the workpiece platform and the surface geometric feature data, the local surface is mapped to the tool coordinate system by calculating the pose transformation matrix of the coating or curing structure relative to the workpiece surface to generate the mapped surface. Step 403: Obtain the real-time coating thickness using the optimal layer thickness and optimal feed rate; based on the local radius of curvature of the mapped surface, obtain the feature spreading radius through approximate calculation; A dynamic equilibrium relationship is constructed based on real-time coating thickness, characteristic spreading radius, resin density, optimal equivalent cone angle, and resin surface tension coefficient. The normal angle of the current surface to be cured is determined. If the normal angle is less than the preset threshold (e.g., 8°), the process returns to step 401 to resynchronize the attitude. If the normal angle is within the preset angle range, the dynamic balance relationship is further verified. If the dynamic balance relationship is valid, the optimal orientation parameter of the current workpiece platform is used as the qualified orientation parameter of the workpiece platform. Otherwise, the process returns to step 401 to resynchronize the attitude. Step 404: Combine the mapped surface, the orientation parameters of the verified workpiece platform, and the kinematic chain definition parameters to generate a discrete trajectory point set through the included angle constraint; Step 405: Use NURBS curves to continuously interpolate the discrete trajectory point set to generate dynamic attitude sequences and continuous spatial motion trajectories.

[0023] Specifically, the process involves obtaining the current forming progress and determining the optimal orientation parameters for the workpiece platform based on the surface geometric feature data and the current forming progress. This process also includes the following steps: Local curvature information (including principal curvature direction and radius of curvature) of the current region to be solidified is extracted from the surface geometric feature data (to determine the local normal vector space distribution of the current region); Based on the current molding progress (i.e., the proportion of the model volume that has been solidified and the position of the current trajectory point in the entire printing task), combined with global geometric constraints, the molding progress prediction result is obtained through prediction. Based on the kinematic chain definition parameters corresponding to the topology type identifier, kinematic calculations are performed to obtain the attitude synchronization results, specifically: If the topology type identifier corresponds to the standard topology (the first kinematic chain is a linear module, and the second kinematic chain is an XY translation + AB composite rotary platform), then the axial direction of the coating or curing structure is regarded as a fixed direction (usually vertically downward). The normal of the surface to be cured is transformed from the local coordinate system of the model to be printed to the coordinate system of the workpiece platform through coordinate transformation. Then, the rotation angle of the AB axis is solved by using inverse trigonometric functions to minimize the angle between the transformed normal and the vertical direction, so as to obtain the attitude synchronization result. If the topology type identifier corresponds to the first deformed topology, then while keeping the workpiece platform fixed, the axial direction of the coating or curing structure is adjusted through two rotation axes to minimize the angle between the coating or curing structure and the normal of the surface to be cured. Then, a set of equations for the normal and the rotation axis angle is established through coordinate transformation, and the set of equations for the normal and the rotation axis angle is solved to obtain the attitude synchronization result. If the topology type identifier corresponds to the second variant topology, then (when detecting whether the current angle of each rotation axis is close to the mechanical limit) the axis closest to the limit is locked near the current angle, and the axis with sufficient margin is used for main attitude adjustment. At the same time, another axis is used as auxiliary compensation. If there are still multiple feasible angle combinations, the one that minimizes the sum of the squares of the angle changes of each axis at adjacent times is selected to obtain the attitude synchronization result. By combining the local curvature information of the current area to be cured, the molding progress prediction results, and the attitude synchronization results, the optimal orientation parameters of the workpiece platform are generated.

[0024] Furthermore, when the topology type identifier corresponds to a standard topology: Let the normal vector of the surface to be cured in the local coordinate system of the model to be printed be... After coordinate transformation to the workpiece platform coordinate system, the transformed normal vector is obtained. The coating or curing structure must be axially fixed (vertically downwards). The angle between the vector and the transformed normal vector is minimized, which is equivalent to making the angle between the vector and the transformed normal vector minimized. and vertical upward direction As close as possible to each other; solve for the AB axis rotating parts: ; in; This represents the rotation angle around the X-axis, i.e., the A-axis; The B-axis represents the rotation angle about the Y-axis; when At that time, Increasing π normalizes the pose. When the topology type identifier corresponds to the first variant topology: Assume the coating head has two axes of rotation: the rotation angle about the Z-axis. and the tilt angle around the X-axis (or Y-axis) The requirement is that, with the workpiece platform fixed, the coating head axially... and With the included angle at its minimum, establish a system of equations: ; in, Indicates the rotation angle around the Z-axis The rotation matrix, Indicates the rotation angle around the X-axis The rotation matrix; Represents the initial axial unit vector of the coated or cured structure, and The initial axis (vertically downward); make Solving for: ; when hour, , It can take any value (usually retaining the value from the previous moment); When the topology type identifier corresponds to the second variant topology: Let the angles of each rotation axis be . Known limits for each axis When solving for attitude synchronization results, first check whether each axis is close to its limit at the current moment. Lock the axis closest to the limit at the current angle value, use the remaining axes with sufficient margin for main attitude adjustment, and use another axis as auxiliary compensation. If there are still multiple feasible angle combinations, select the one that minimizes the sum of the squares of the angle changes of each axis at adjacent moments. ; in, Indicates the rotation axis index. This represents the angle value of the i-th rotation axis at time t. Indicates the i-th rotation axis at The angle value at that moment, Indicates the sampling time; The constraints are: forward kinematic equations (Desired pose) and constraint inequalities; this optimization problem can be solved in real time using numerical algorithms such as Sequential Quadratic Programming (SQP) or Iterative Closest Point (ICP). Take the motion control cycle.

[0025] The purpose of determining the normal angle is to prevent the resin from dripping directly onto the nearly horizontal downward surface due to gravity and failing to form a liquid film. When the normal angle is less than a preset threshold (e.g., 8°), it indicates that the curved surface is too close to the horizontal lower surface state, and it is necessary to return to step 401 to readjust the orientation of the workpiece platform to ensure that the resin can adhere stably. The expression for the dynamic equilibrium relationship is: ; in, Represents gravitational acceleration. Indicates resin density, Indicates the real-time coating thickness. Indicates the included angle of the normals. This represents the surface tension coefficient of the resin. Indicates the feature spreading radius; It should be noted that the normal angle determination takes precedence over the dynamic balance relationship verification. If the normal angle is less than a preset threshold (e.g., 8°), the process returns directly to step 401 to re-synchronize the attitude. Dynamic balance relationship verification only proceeds when the normal angle is within the preset angle range. When the dynamic balance relationship is valid, the optimal orientation parameter of the current workpiece platform is used as the qualified orientation parameter for the workpiece platform. If the dynamic balance relationship is invalid, the process returns to step 401 to re-synchronize the attitude. The physical significance of this dynamic equilibrium relationship lies in ensuring that the resin film, during its continuous movement along the curved surface, can resist the flow caused by the tangential component of gravity through its own surface tension. Specifically, the left side of the inequality sign represents the gravity-driven pressure gradient of the resin film along the tangential direction of the curved surface (the tendency for the resin to flow downwards), while the right side represents the capillary spreading pressure generated by surface tension and surface curvature (the tendency for the resin to spread and maintain the stability of the liquid film). When this inequality holds, the surface tension is sufficient to suppress sagging caused by gravity, ensuring that the resin maintains a uniform and continuous liquid film shape without rupture or accumulation during dynamic movement. This is a physical property guarantee condition (soft constraint) for molding quality. If this condition is not met, it indicates that the current resin material, coating thickness, and surface curvature are mismatched, and the equilibrium relationship needs to be restored by reducing the feed rate or reducing the layer thickness.

[0026] Furthermore, the feature spreading radius is calculated in the following way: Extract the two principal curvature radii from the current solidified point on the mapped surface, and then calculate the equivalent curvature radius using the equivalent curvature radius formula: ; in, Represents the equivalent radius of curvature. and These are the two principal curvature radii at the current solidification point; The feature spreading radius is obtained by using the equivalent radius of curvature and the real-time coating thickness: .

[0027] Specifically, by combining the mapped surface, the orientation parameters of the verified workpiece platform, and the kinematic chain definition parameters, a discrete trajectory point set is generated through angular constraints. This process also includes the following steps: The current kinematic chain definition parameters are used as limit constraints; the actual angle values ​​of each rotation axis of the current kinematic chain are determined based on the verified workpiece platform orientation parameters; under the limit constraints, the rotational tangential direction vector is calculated using the actual angle values ​​of each rotation axis of the current kinematic chain; the rotational tangential direction vector is normalized to obtain the normalized rotational tangential direction vector. Specifically, for the standard topology (AB axis), the rotational tangential direction = (B-axis angular velocity × workpiece radial unit vector) + (A-axis angular velocity × workpiece axial unit vector). On the feed path in the mapped surface, calculate the angle between the actual feed direction of each trajectory point on the feed path and the normalized rotational tangential direction vector at the corresponding moment; select trajectory points that satisfy the preset angle range as the selected trajectory points; after traversing all trajectory points, integrate the selected trajectory points to obtain a discrete trajectory point set.

[0028] Furthermore, please refer to Table 2. This invention uses the same dental full crown model for comparative testing. As shown in Table 2: Edge precision (CMM measurement): After removing the support in the traditional support printing process, the average gap at the edge of the shoulder is 42μm; using the supportless continuous molding of this invention, the average gap is reduced to 18μm, and the standard deviation is reduced by 60%. Surface roughness (Ra): After traditional process of removing support and polishing, Ra≈1.6μm; The surface of the one-time molding of the present invention is Ra≈0.7μm, without the need for additional polishing; Curing uniformity (FTIR): The absence of support shielding reduced the standard deviation of double bond conversion rate distribution from 4.2% to 1.8%, and improved interlayer bond strength by approximately 35%.

[0029] Table 2. Comparative test results conducted using the same dental crown model.

[0030] Step 5: Based on the dynamic posture sequence and continuous spatial motion trajectory, drive the first kinematic chain and the second kinematic chain to complete the five-axis unsupported continuous photopolymerization molding.

[0031] Furthermore, based on dynamic posture sequences and continuous spatial motion trajectories, the linear module is driven to control the movement of the coating and curing structure according to the continuous spatial motion trajectory, and the composite rotary platform is driven to control the movement of the workpiece platform according to the dynamic posture sequence; the resin self-adheres to the surface to be cured under the action of gravity and surface tension, and continuously cross-links and forms under ultraviolet light irradiation; at the same time, the entire printing process does not contain any independent Z-axis peeling action.

[0032] Please see Figure 2 This invention also provides a five-axis unsupported continuous photopolymerization molding system, the system comprising: The feature data acquisition module is used for: Obtain surface geometric feature data based on the 3D data of the model to be printed; The topology type identifier generation module is used for: Based on the mechanical layout of the device, a predefined topology is used to obtain the kinematic chain definition parameters and generate a topology type identifier. The parameter acquisition module is used for: Obtain the resin viscosity value, and based on the resin viscosity value, match the optimal layer thickness, optimal feed rate, optimal equivalent cone angle, resin density, and resin surface tension coefficient from the preset parameter table; The kinematic joint optimization module is used for: By utilizing surface geometric feature data, topology type identifiers, kinematic chain definition parameters, optimal layer thickness, optimal feed rate, optimal equivalent cone angle, resin density, and resin surface tension coefficient, a dynamic equilibrium relationship between the surface to be cured and the resin coating is constructed. Based on the dynamic equilibrium relationship between the surface to be cured and the resin coating, combined with angular constraints, dynamic posture sequences and continuous spatial motion trajectories are generated through kinematic joint optimization. Curing module, used for: Based on dynamic posture sequences and continuous spatial motion trajectories, the first and second motion chains are driven to complete five-axis unsupported continuous photopolymerization molding.

[0033] It should be understood that various parts of the present invention can be implemented in hardware, software, firmware, or a combination thereof. In the above embodiments, multiple steps or methods can be implemented in software or firmware stored in memory and executed by a suitable instruction execution system. For example, if implemented in hardware, as in another embodiment, it can be implemented using any one or a combination of the following techniques known in the art: discrete logic circuits having logic gates for implementing logical functions on data signals, application-specific integrated circuits (ASICs) having suitable combinational logic gates, programmable gate arrays (PGAs), field-programmable gate arrays (FPGAs), etc.

[0034] In the description of this specification, references to terms such as "one embodiment," "some embodiments," "example," "specific example," or "some examples," etc., indicate that a specific feature, structure, material, or characteristic described in connection with that embodiment or example is included in at least one embodiment or example of the invention. In this specification, the illustrative expressions of the above terms do not necessarily refer to the same embodiment or example. Furthermore, the specific features, structures, materials, or characteristics described may be combined in any suitable manner in one or more embodiments or examples.

[0035] The embodiments described above are merely illustrative of several implementations of the present invention, and while the descriptions are specific and detailed, they should not be construed as limiting the scope of the present invention. It should be noted that those skilled in the art can make various modifications and improvements without departing from the concept of the present invention, and these modifications and improvements all fall within the scope of protection of the present invention. Therefore, the scope of protection of this patent should be determined by the appended claims.

Claims

1. A five-axis unsupported continuous photopolymerization molding method, characterized in that, The method includes the following steps: Step 1: Obtain surface geometric feature data based on the 3D data of the model to be printed; Step 2: Based on the mechanical layout of the equipment, a predefined topology is used to obtain the kinematic chain definition parameters and generate a topology type identifier. Step 3: Obtain the resin viscosity value, and based on the resin viscosity value, match the optimal layer thickness, optimal feed speed, optimal equivalent cone angle, resin density, and resin surface tension coefficient from the preset parameter table. Step 4: Using surface geometric feature data, topology type identifier, kinematic chain definition parameters, optimal layer thickness, optimal feed rate, optimal equivalent cone angle, resin density, and resin surface tension coefficient, a dynamic equilibrium relationship between the surface to be cured and the resin coating is constructed. Based on the dynamic equilibrium relationship between the surface to be cured and the resin coating, combined with the included angle constraint, a dynamic posture sequence and a continuous spatial motion trajectory are generated through kinematic joint optimization. Step 5: Based on the dynamic posture sequence and continuous spatial motion trajectory, drive the first kinematic chain and the second kinematic chain to complete the five-axis unsupported continuous photopolymerization molding.

2. The five-axis unsupported continuous photopolymerization molding method according to claim 1, characterized in that, In step 2, a predefined topology is used based on the mechanical layout of the device. Kinematic chain definition parameters are obtained through this predefined topology, and a topology type identifier is generated. This topology type identifier is divided into three types: standard topology, first variant topology, and second variant topology. The standard topology is defined as follows: the first kinematic chain is a linear module, and the second kinematic chain is a composite rotary platform. The first variant topology is defined as follows: the first kinematic chain is a coating head with rotational degrees of freedom, and the second kinematic chain is a fixed or translational platform. The second variant topology is defined as a five-axis drive configuration with redundant rotational degrees of freedom; wherein the first kinematic chain is used to control the spatial movement of the coating or curing structure, and the second kinematic chain is used to control the pose adjustment of the workpiece platform.

3. The five-axis unsupported continuous photopolymerization molding method according to claim 2, characterized in that, In step 4, surface geometric feature data, topology type identifier, kinematic chain definition parameters, optimal layer thickness, optimal feed rate, optimal equivalent cone angle, resin density, and resin surface tension coefficient are used to construct a dynamic equilibrium relationship between the surface to be cured and the resin coating. Based on this dynamic equilibrium relationship, and combined with angular constraints, a dynamic posture sequence and a continuous spatial motion trajectory are generated through kinematic joint optimization. The specific steps are as follows: Step 401: Obtain the current forming progress, and determine the optimal orientation parameters of the workpiece platform based on the surface geometric feature data and the current forming progress; Step 402: Using the optimal orientation parameters of the workpiece platform and the surface geometric feature data, the local surface is mapped to the tool coordinate system by calculating the pose transformation matrix of the coating or curing structure relative to the workpiece surface to generate the mapped surface. Step 403: Obtain the real-time coating thickness using the optimal layer thickness and optimal feed rate; based on the local radius of curvature of the mapped surface, obtain the feature spreading radius through approximate calculation; A dynamic equilibrium relationship is constructed based on real-time coating thickness, characteristic spreading radius, resin density, optimal equivalent cone angle, and resin surface tension coefficient. Under the condition of satisfying the dynamic balance relationship, the normal angle of the current surface to be cured is determined by the preset angle range. When the normal angle of the current surface to be cured is within the preset angle range, the optimal orientation parameter of the current workpiece platform is taken as the orientation parameter of the workpiece platform that passes the inspection. Otherwise, return to step 401 to re-synchronize attitude; Step 404: Combine the mapped surface, the orientation parameters of the verified workpiece platform, and the kinematic chain definition parameters to generate a discrete trajectory point set through the included angle constraint; Step 405: Use NURBS curves to continuously interpolate the discrete trajectory point set to generate dynamic attitude sequences and continuous spatial motion trajectories.

4. The five-axis unsupported continuous photopolymerization molding method according to claim 3, characterized in that, The process involves obtaining the current forming progress and determining the optimal orientation parameters for the workpiece platform based on the surface geometry data and the current forming progress. Specifically, this includes the following steps: Local curvature information of the current region to be solidified is extracted from surface geometric feature data; Based on the current molding progress and combined with global geometric constraints, the molding progress prediction result is obtained through prediction. Based on the kinematic chain definition parameters corresponding to the topology type identifier, kinematic calculations are performed to obtain the attitude synchronization results, specifically: If the topology type identifier corresponds to the standard topology, the axial direction of the coating or curing structure is regarded as a fixed direction. The normal of the surface to be cured is transformed from the local coordinate system of the model to be printed to the coordinate system of the workpiece platform through coordinate transformation. Then, the rotation angle of the AB axis is solved by inverse trigonometric function so that the angle between the transformed normal and the vertical direction is minimized, so as to obtain the attitude synchronization result. If the topology type identifier corresponds to the first deformed topology, then while keeping the workpiece platform fixed, the axial direction of the coating or curing structure is adjusted through two rotation axes to minimize the angle between the coating or curing structure and the normal of the surface to be cured. Then, a set of equations for the normal and the rotation axis angle is established through coordinate transformation, and the set of equations for the normal and the rotation axis angle is solved to obtain the attitude synchronization result. If the topology type identifier corresponds to the second variant topology, the axis closest to the limit is locked near the current angle, and the main attitude is adjusted using the axis with sufficient margin, while the other axis is used as auxiliary compensation to obtain the attitude synchronization result. By combining the local curvature information of the current area to be cured, the molding progress prediction results, and the attitude synchronization results, the optimal orientation parameters of the workpiece platform are generated.

5. The five-axis unsupported continuous photopolymerization molding method according to claim 4, characterized in that, Based on real-time coating thickness, characteristic spreading radius, resin density, optimal equivalent cone angle, and resin surface tension coefficient, a dynamic equilibrium relationship is constructed. The expression for the dynamic equilibrium relationship is as follows: ； in, Represents gravitational acceleration. Indicates resin density, Indicates the real-time coating thickness. Indicates the included angle of the normals. This represents the surface tension coefficient of the resin. Indicates the feature spreading radius.

6. The five-axis unsupported continuous photopolymerization molding method according to claim 5, characterized in that, Combining the mapped surface, the orientation parameters of the verified workpiece platform, and the kinematic chain definition parameters, a discrete trajectory point set is generated through angular constraints. This process also includes the following steps: The current kinematic chain definition parameters are used as limit constraints; the actual angle values ​​of each rotation axis of the current kinematic chain are determined based on the verified workpiece platform orientation parameters; under the limit constraints, the rotational tangential direction vector is calculated using the actual angle values ​​of each rotation axis of the current kinematic chain; the rotational tangential direction vector is normalized to obtain the normalized rotational tangential direction vector. On the feed path in the mapped surface, calculate the angle between the actual feed direction of each trajectory point on the feed path and the normalized rotational tangential direction vector at the corresponding moment; select the trajectory points that satisfy the preset angle range as the selected trajectory points. After traversing all trajectory points, the selected trajectory points are integrated to obtain a discrete trajectory point set.

7. The five-axis unsupported continuous photopolymerization molding method according to claim 6, characterized in that, In step 403, when determining the normal angle of the current surface to be cured, the preset angle range is a normal angle greater than or equal to 8°; when the normal angle is less than 8°, it is determined that the resin cannot be stably attached under the current posture, and the process returns to step 401 to resynchronize the posture; when the normal angle is greater than or equal to 8°, the process enters the dynamic balance relationship verification.

8. A five-axis unsupported continuous photopolymerization molding system, characterized in that, The system employs the five-axis unsupported continuous photopolymerization molding method according to any one of claims 1 to 7, and the system comprises: The feature data acquisition module is used for: Obtain surface geometric feature data based on the 3D data of the model to be printed; The topology type identifier generation module is used for: Based on the mechanical layout of the device, a predefined topology is used to obtain the kinematic chain definition parameters and generate a topology type identifier. The parameter acquisition module is used for: Obtain the resin viscosity value, and based on the resin viscosity value, match the optimal layer thickness, optimal feed rate, optimal equivalent cone angle, resin density, and resin surface tension coefficient from the preset parameter table; The kinematic joint optimization module is used for: By utilizing surface geometric feature data, topology type identifiers, kinematic chain definition parameters, optimal layer thickness, optimal feed rate, optimal equivalent cone angle, resin density, and resin surface tension coefficient, a dynamic equilibrium relationship between the surface to be cured and the resin coating is constructed. Based on the dynamic equilibrium relationship between the surface to be cured and the resin coating, combined with angular constraints, dynamic posture sequences and continuous spatial motion trajectories are generated through kinematic joint optimization. Curing module, used for: Based on dynamic posture sequences and continuous spatial motion trajectories, the first and second motion chains are driven to complete five-axis unsupported continuous photopolymerization molding.

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