The mechanism movement of parallel robots or parallel machine tools is more complicated, and the working space is mostly irregular three-dimensional space, and the displacement in the operating space and the pose change of the working space are nonlinear. Through the solid modeling and kinematics simulation of the parallel machine tool, using computer animation technology to simulate the machining process of the machine tool, the static or dynamic interference problem caused by the unreasonable structural size of the machine tool design can be found in advance, and the correct result of the machining path planning of the machine tool is verified. Sex, to prevent collisions or machining areas that cannot be realized by the machine itself, to avoid damage to the machine.

This paper uses Windows2000 as the development platform, uses Visual C++ and 3D graphics software standard interface OpenGL tool to develop the simulation software of parallel machine tool. Using computer graphics technology, it simulates the structure and mechanism motion of parallel machine tool through animation form. The machine structure and motion principle are illustrated. The three-dimensional motion simulation is basically the same as the real machine tool, which provides a reliable guarantee for the smooth development of the new five-degree-of-freedom parallel machine tool.

2 computer simulation tools

OpenGL OpenGL is a three-dimensional computer graphics and model library <5>, the Open Graphic Library. Due to its excellent performance in 3D realistic graphics production, OpenGL has become the next-generation industry standard 3D computer graphics software interface.

In addition to providing basic geometric features (points, lines, polygons), OpenGL's graphics library also provides regular quadratic surfaces (such as spheres, cones, polyhedra, etc.) and complex curved surfaces (such as Bezi2 er , Nurbs). Etc.) The drawing function can be used to build complex 3D models and set lighting models and material properties to produce more realistic images. OpenGL with graphics blanking function, using Z-buffer (Z2buffer) technology for depth testing, surface blanking, enhance the realism of graphics. In addition, OpenGL also has a series of special processing functions such as color, bitmap, texture, blending, anti-aliasing, etc., making the simulation environment more realistic. The application of OpenGL reduces the programming amount of the simulation system, and the developer does not need to master a large amount of graphics knowledge, but can concentrate on studying difficult algorithm problems and reduce the development workload.

In addition, OpenGL is hardware-independent and can be implemented on different hardware platforms, making it easy to port applications to different operating systems. Because it is an application program interface - 3D API, OpenGL can be called by program, and the simulation system can be integrated into the control system to realize real-time control of machine tool motion simulation and improve system interactivity and operability.

3 Parallel Machine Tool Features and Mathematical Model of Mechanism Motion

The structural characteristics of parallel machine tools and the mathematical model of kinematics are the basis of solid modeling and motion simulation, so specific analysis is needed.

311 five-degree-of-freedom parallel machine features

The five-degree-of-freedom parallel machine tool mechanism is composed of a fixed platform, a moving platform, and a branch connecting the fixed platform and the moving platform. The characteristic is that the fixed platform is branched and moved by five branches of the same drive branch UPS (Hook hinge; mobile sub-ball pair) and a constrained branch PRPU (moving vice? rotating vice? mobile vice? Hooke hinge). The platforms are connected. The mechanism can realize three-dimensional movement and two-dimensional rotation, and has the advantages of large rigidity-to-weight ratio, simple structure, good dynamic performance and large working space, and the kinematics inverse solution is very simple, and the control algorithm is easy to implement.

312 mechanism motion mathematical model

The coordinate system is established on the upper and lower platforms respectively. The fixed coordinate system { A } is fixed on the fixed platform, and the dynamic coordinate system { B } is established on the moving platform. The five-degree-of-freedom parallel machine tool movement consists of five drive branches driving the movement of the machine platform and the follow-up of the constrained branches. The pose parameters of the moving platform relative to the fixed platform are expressed as (AX BO, AY BO, AZ BO, α, β), where the position coordinates of the origin OB of { B } in { A } are expressed as AP BO = < AX BO , AY BO, AZ BO > T, { B } The relative Euler angle with respect to { A } is (α, β).

From the actual structural dimensions of the machine tool, the length l (i = 1 , 2 ,..., 5) of the five drive branches can be found as li = fi(AX BO, AY BO, AZ BO, α, β; W , r A, r B, θ, using the D? H coordinate to analyze the intermediate constraint branch PRPU branch (variables d 1, a 2, θ2, θ3, θ4 are the motion parameters of each motion pair, constant a 4 is the mechanism parameter), The motion model for obtaining the intermediate branch is d 1 = AZ BO + a 4 sβa 2 = (AX BO - a 4 cacβ) 2 + (AY BO - a 4 sacβ) 2θ2 = arctan AY BO - a 4 sacβA X BO - a 4 Cacβθ3 =α-θ2θ4 = -β(2) From the pose parameters of the moving platform, the motion of each branch of the machine tool can be determined. Using these mathematical models to drive the linkage of each branch, the motion simulation of the machine tool can be realized.

4 parallel machine model construction

Through the above analysis of the structural characteristics of the parallel machine tool, the model of the machine tool can be established according to the actual structural parameters. In the modeling, the machine parts are first simplified according to their main physical features, and then these parts are assembled into a complete machine. The five-degree-of-freedom parallel machine tool structure includes fixed parts for the bed and the table, the moving parts as the moving platform, five driving branches and one constraining branch. Since the fixed parts are stationary during the motion simulation process, and the moving parts move according to the planned pose and speed, the two models need different methods in the model construction in order to improve the effect of the machine simulation.

All complex 3D objects drawn by OpenGL are made up of a certain number of basic graphical elements. According to the structural size of the parallel machine tool, the relative position of the main components in space can be calculated, and then the basic modeling function provided by the OpenGL graphic function library is used to clearly express the relative positional relationship and motion level of each component by matrix stacking technology. Relationships to build a solid model of a parallel machine tool.

411 Machine Tool Fixed Parts Model Construction The machine tool fixed parts are stationary. During the movement of the machine tool, these parts are no longer refreshed, which can reduce the amount of data displayed by the simulation and increase the display speed. The bed components are usually constructed with regular quadric surfaces such as cubes and cylinders. The base and column adopt the cuboid model and directly construct the functions in OpenGL. The upper platform structure of the bed is more complicated. It is difficult to realize the Boolean difference of the entity due to OpenGL. The operation can be combined by a plurality of simple regular shapes, and the modeling of the upper platform is realized by using the mosaic technology of the complex polygon. Similarly, the T-slot on the machine table can be simplified by a combination of multiple cuboids.

412 Machine Tool Moving Parts Model Construction Moving parts need to be refreshed in real time during machine tool movement, so they can be modeled by input parameters. During the movement of the machine tool, the parameter changes are used to determine the geometric position of the moving object in the space, and the position changes of the moving parts such as rotation and translation are realized. The moving platform can be simplified into a cone, and the electric spindle and the milling cutter mounted thereon are constructed of a cylinder. The driving branch itself is composed of a swinging rod and a telescopic rod, wherein the swinging rod is constructed by a hollow cylinder, and the telescopic rod is constructed of a solid cylinder; the swinging rod is connected to the platform of the bed by a Hooke hinge, and the Hooke hinge is composed of a cylinder and a hollow elliptical cylinder. The combination is made up; the telescopic rod is connected to the moving platform through the ball joint, and the ball joint is simplified into a sphere. The first moving auxiliary member in the constrained branch is a sliding block, which is composed of a rectangular parallelepiped. The rotating auxiliary member is composed of a cube, a solid cylinder and a hollow cylinder, and the second moving auxiliary member is composed of a solid cylinder. The hinge is a combination of a cylinder and a hollow elliptical cylinder.

5 parallel machine tool mechanism motion simulation design

After the kinematics analysis of the parallel machine tool, the mathematical model of the machine tool kinematics is established, which can grasp the motion characteristics of the parallel machine tool. The motion simulation of the parallel machine tool mechanism is based on the mathematical model of the mechanism motion. The model provided by OpenGL is used to perform various matrix transformations such as rotation transformation, translation transformation and scaling transformation in the space to realize the motion simulation of the machine tool. In the process of parallel machine tool movement, the movement of each component is not isolated, but has a certain relationship with the movement of other components, so it is necessary to ensure the coordination of the movement of each component.

511 component motion simulation design The motion simulation of the machine tool is mainly through the trajectory planning of the machining process, and the pose of the jog platform at each discrete time is obtained. After the posture of the moving platform is determined, according to the motion constraint relationship, the pose of the driving branch is also determined accordingly. One end of the driving branch is determined by the position of the Hook hinge of the platform on the machine bed, and the other end is determined by the position of the ball joint on the moving platform, the direction of which is through the connection between the corresponding Hook hinge and the ball joint; the components of the constraining branch The pose can also be determined.

Machine tool motion simulation is mainly realized by coordinate transformation. The coordinate system used in OpenGL is the world coordinate system and the local coordinate system. The world coordinate system is a right-hand coordinate system, but the world coordinate system is different from the general Cartesian coordinate system in mathematics, and its X-axis is from left to right. The Y axis is from bottom to top, and the Z axis is from inside to outside. The local coordinate system is relative to the modeled object. The origin of the coordinate is often the centroid of the object and moves with the movement of the object. The coordinate transformation is used to realize the relative position and geometric transformation between the various component models of the machine tool. The orientation of the local coordinate system is unchanged during the translation transformation. The only change is the origin position of the local coordinate system. The rotation transformation changes the orientation of the local coordinate system of the object. Once the orientation of the coordinate system is changed, it affects the drawing of the object in the future.

Since the actual machine coordinate system and fixed coordinate system are different from the world coordinate system and local coordinate system in OpenGL, the transformation of the position of each component of the machine tool between these different coordinate systems becomes the key to machine motion simulation. According to the mathematical model of the machine tool movement, the pose parameters of the moving parts of the machine tool in the fixed coordinate system of the machine tool can be obtained based on the pose parameters of the moving platform during the movement of the machine tool, and then these pose parameters are converted into the coordinate system representation in OpenGL. Form, using the translation transformation and rotation transformation of the coordinate system, the model pose of the various components of the machine tool during the movement can be obtained. The position change of each component is realized by translation transformation, and the attitude change is realized by rotation transformation. The same processing is performed for each set of pose parameters, and then the machine model image is calculated and generated and refreshed, and the machine motion simulation is realized.

512 mechanism constraint and interference collision test analysis Parallel machine tool and traditional machine tool structure form a big difference, the movement of key components is not as "rule" as traditional machine tools, parallel machine tool between the branches during the movement and other parts of the machine tool They are mutually restrained, and interference may occur when moving to certain positions, the so-called "stuck" phenomenon.

There are 6 hinges on the moving platform of the machine. There are 6 hinges on the fixed platform (actually one moving pair is above the fixed platform), and the existing constraints mainly include the longest and shortest rod length constraint (the telescopic rod) or the maximum and minimum stroke (slider). Constraint, ball hinge and Hook hinge limit swing angle constraints and interference constraints between components. Due to structural limitations, theoretical analysis and actual manufacturing of machine tools have certain differences. For the rod length constraint and the slider stroke constraint, it is necessary to ensure that the actual rod length and stroke are within the shortest and longest stroke limit values, and the actual length can be calculated according to the mathematical model of the mechanism, and then compared with the given limit range and judgment. Since the maximum swing angle of the ball joint and the Hooke hinge is determined by the specific structure of each motion pair, when determining the maximum swing angle constraint of the ball joint and the Hooke hinge, the direction vector of each drive rod can be moved. The dot product of the fixed plate normal vector is used to find the swing angle of each drive rod with respect to the moving and fixed platform, and compare this swing angle with the maximum swing angle allowed by the Hooke hinge and the ball joint at the hinge of the moving and fixed platforms. judgment. When the posture of the moving platform changes, collision interference may occur between the connecting rods, the connecting rod and the electric spindle between the moving and fixed platforms, and the intermediate constraint branch of the machine limits the rotation of the moving platform around its own normal line. There is generally no interference between the five drive branches and between the middle branch and the five drive branches; since the electric spindle and the drive branch are both simplified into a cylinder, the interference that may occur between the two can be divided into two types: The two cylinder axes intersect, the distance between the intersection point from the upper end surface of the electric main shaft and the angle of the two intersecting axes conform to a specific geometric relationship; the other is the difference between the two cylinder axes, the vertical line and the two line segments The axis of the cylinder intersects the end faces of the two lines, and the length of the male perpendicular is less than the sum of the radii of the two cylinders.

By checking whether interference occurs between the components, it is possible to verify the rationality of the machine tool structure design and check whether the trajectory planning result of the machine tool processing is correct.

Real-time strategy analysis of 513 mechanism motion simulation The real-time performance of motion simulation of the mechanism plays an important role in the motion simulation effect of parallel machine tools. Some strategies are proposed to improve the real-time performance of the simulation and enhance the effect of motion simulation.

(1) Adopt local refresh technology. Partial refresh refers to the calculation and refresh display of the moving part model part during the movement of the machine tool, while the fixed part remains unchanged, so that the processing can avoid the repeated refresh display of the picture, effectively solving the real-time performance and calculation amount of the animation display. The contradiction between. You can use OpenGL's stencil buffering technology to block the display on the screen by pixel operation to block specific areas on the screen. You can set the fixed parts in the machine model to the stencil buffer to not refresh the displayed part, while the moving parts are set. In order to refresh the displayed part, during the simulation process, the stencil buffer tests each generated picture and refreshes the displayed part of the graphic to improve the display speed of the simulation.

(2) Adopt display list and double buffer technology. Since OpenGL uses polygons to build solid models, the machine model refreshes a large amount of data, and display list technology can effectively increase the display speed. The display list is a set of pre-stored cache commands that can be called anywhere, without memory management, and executed immediately in order, reducing time overhead and improving drawing display efficiency. The model data of the moving part of the machine tool is compiled and put into the display list, and then the display list is sequentially called during the movement, thereby reducing the execution time and increasing the display speed. In addition, OpenGL utilizes double-buffer technology for animation display. The double cache includes a background cache and a front-end cache. The background cache calculates the scene, generates a picture, and the foreground cache displays the picture that the background buffer has generated, thereby improving the speed of the animation real-time refresh display.

(3) Adopt a high-precision time function. In Windows applications, hardware-related high-resolution timers supported in the Windows operating system can be used. By calling two API functions QueryPerformanceFrequency() and QueryPerformance Counter(), high-performance timers can be provided. Achieve 1μs to improve the real-time performance of motion simulation.

6 parallel machine tool simulation implementation

Based on the previous theoretical analysis and technical method research, the simulation system of parallel machine tools was developed.

In the parallel machine tool simulation system, the workpiece blank is first transferred, the machining tool is selected, and the tool position data required for machining is read. The general CNC machining code format (XC, YC, ZC, θx, θy, θz) is used, among which PC = < XC, YC, ZC > T represents the position coordinate of the center C of the tool bottom, (θx, θy, θz) represents the direction angle of the tool axis vector of the tool attitude; then the tool position data is processed to obtain the position of the machine platform The pose data is calculated by using the mathematical model of the mechanism motion to calculate the pose change data of each of the drive branches corresponding to each tool point and each of the motion components in the constraint branch. The data is processed into data that can be recognized by the simulation system, and is in the form of a linked list. Stored in memory, each node of the linked list saves a set of pose data; finally, the high-precision timing function is used to traverse the linked list data in each cycle, and each set of data is processed to generate a new machine motion model picture, using double buffer pair The screen is refreshed and displayed. After reading a group, displaying a group, and then reading the next group, this cycle is performed to realize the mechanism motion simulation of the machine tool. It can be seen that the realism of the graphics during the motion is strong. The application of the real-time strategy makes the motion of the components continuous and smooth, without pauses. The interference test effectively prevents the damage caused by the unreasonable motion trajectory planning.

A circular trajectory with a diameter of 200 mm was drawn using the developed machine tool prototype and simulation system. The prototype of the machine tool is 1018s, the curvature of the trajectory is smooth and the fitting is good. The simulation system takes 12s, the trajectory is closed, and the roundness is good, which is basically consistent with the experimental results of the machine tool.

7 conclusion

The realization method of parallel machine tool solid modeling and motion simulation better solves the realistic graphic display and animation display in machine tool motion simulation. By establishing a mathematical model of parallel machine tool motion, it provides a basis for the motion simulation of the machine tool. The parallel machine tool simulation system was developed using OpenGL graphics standard. The simulation system does not rely on the existing general CAD software, and can be operated independently or integrated into the machine control system to realize the integration of machine control and simulation. The circular trajectory is drawn by the simulation system and the machine tool prototype respectively, and the time used is close, and the effect is basically the same. The simulation system has a strong sense of reality. The motion simulation and interference test provide a strong guarantee for the motion research, control research and structural design of the machine tool, and have certain practical value.

(Finish)

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