A systematic design method combining door glass production and motion verification

Abstract

The present invention discloses a systematic design method combining door glass production and motion verification, including the following steps: inputting CAS into the modeling; fitting the front and rear boundary spiral lines of the glass surface according to CAS; confirming the guide lines of each door according to the window surface of each door of the modeling and the fitted spiral lines; using the obtained glass spiral lines and guide lines to produce high-precision glass spiral surfaces, and trimming the upper stop point of the glass; decomposing the spiral motion of any point on the glass surface into two steps: first, the rotational motion around the axis, and then the translational motion along the axis to determine the lower stop point position. The present invention can be implemented through the same design module to achieve an integrated design from door glass production to motion verification. When a new modeling appears, it is only necessary to replace the corresponding modeling reference line, and through parameter association, the new glass surface and glass motion trajectory can be fitted. This method greatly saves design time and verification time while ensuring the quality of the glass fitting surface.

Description

Technical Field

[0001] The invention belongs to the field of automobile design accessory design, and in particular is a systematic design method combining door glass production and motion verification. Background Art

[0002] In the feasibility study of the modeling, the door glass is the basis of the entire door system design and needs to be output with the highest priority. The output content includes: glass spiral surface, the position status of the upper and lower stop points of the glass (for the verification of other environmental parts). With the development of the times, the modeling styles of door glass are becoming more and more diverse, which puts higher requirements on the fitted glass spiral surface. At present, the widely used method is to fit the glass spiral surface through a double helix curve.

[0003] If the curvature of the shape boundary line is too small, the fitted glass spiral surface will be in poor condition, which will affect the functionality of the glass lifting and the formability of the glass. Multiple feedback to the shape changes will also increase the repetition time and reduce efficiency. If the fitted glass spiral surface of the front and rear doors has too large a deviation in the Y direction in the B-pillar area, it may affect the appearance of the window frame (the window frame will be visually uneven).

[0004] After the glass spiral surface is obtained by fitting, it is often necessary to trim the glass top stop point in accordance with the shape by coordinating with the window frame and window sill sealing strip. At the same time, it is also necessary to further confirm the position of the glass when it drops to the bottom stop point. This step is usually achieved by the motion simulation (DMU) of the door glass. Due to the inherent module properties of the DMU, ​​some unique problems will arise, such as: switching of CATIA modules, the inherent properties of the DMU module must divide the moving parts and interfaces into different parts, the position after movement is not convenient for independent output of results, and when the results do not meet the requirements and the original data is adjusted, the DMU needs to be rebuilt, which is inefficient, etc.

[0005] From the current situation, the accuracy of the fitted glass spiral surface and the deviation from the modeling will still lead to repeated modeling. At the same time, the glass spiral surface fitting and glass motion verification are carried out separately, and the glass motion verification process is cumbersome. On the one hand, it is not conducive to repeated work. On the other hand, it is slow for novices to get started. If it is not used for a long time, it is easy to forget the operation steps.

[0006] With the development of the times, the styling styles of car door glass are becoming more and more diversified, which puts higher requirements on the manufacturing of fitted glass. At the same time, as the basis of the entire door system design, car door glass needs to be given top priority output. The high-quality fitting of the glass spiral line and the rapid manufacturing and updating of the upper and lower movement stop points of the glass have become the key and difficult points in the design and development process. Summary of the invention

[0007] In view of the problems existing in the background technology, the purpose of the present invention is to provide a systematic design method combining door glass production and motion verification. This method can not only accurately fit the glass spiral surface, but also further determine the glass surface (upper dead point) and the corresponding lower dead point position when it descends. This method can break away from the existing complexity, efficiently serve the automobile door design, and become the focus of improving technology.

[0008] To achieve the above object, the present invention provides a systematic design method combining door glass manufacturing and motion verification, which is characterized by comprising the following steps:

[0009] S1, modeling input CAS;

[0010] S2, fitting the spiral lines of the front and rear boundaries of the glass surface according to CAS;

[0011] S3, confirming the guide lines of each door according to the window surface of each door and the fitted spiral line;

[0012] S4, using the obtained glass spiral line and guide line to make a high-precision glass spiral surface and trim the glass top dead point;

[0013] S5, decompose the spiral motion of any point on the glass surface into two steps: first, the rotational motion around the axis, and then the translational motion along the axis to determine the bottom dead point position.

[0014] As a preferred solution, in order to reduce repetition time and improve efficiency, it is necessary to preliminarily judge the CAS status when inputting the shape. Specifically, four condition checks are required to determine whether the shape meets the requirements of high-quality glass surface fitting:

[0015] ① The curvature radius R1 of the front and rear boundaries of the shaped glass surface must be greater than the predicted value;

[0016] ②The curvature radius R2 of the window sill sealing strip must be greater than the predicted value;

[0017] ③ The inclination angle α of the B-pillar window frame of the shape must be smaller than the predicted value;

[0018] ④The front and rear borders of the glass must be parallel;

[0019] When the glass surface provided by the shape meets the above four conditions, start designing the glass surface.

[0020] Preferably, the predicted value in the above requirement ① is 1000mm.

[0021] Preferably, the predicted value in the above requirement ② is 15000mm.

[0022] Preferably, the predicted value in the above requirement ③ is 15°

[0023] Preferably, step S2 includes:

[0024] S201, obtaining the spiral axis of the glass surface by fitting the upper and lower endpoints and the midpoint of the front and rear boundaries of the glass surface;

[0025] S202, calculating the front and rear boundary spiral lines according to the formula based on the glass spiral axis O and the midpoints of the front and rear boundaries:

[0026]

[0027] Among them, α is the rotation angle, P is the pitch of the spiral line where the point is located, Ri is the distance between the point and the spiral axis, and S is the length of the spiral line motion;

[0028] By adjusting the pitch P value, when the deviation value between the fitted spiral line and the modeling boundary meets the preset conditions, the spiral lines at the front and rear boundaries of the glass surface can be confirmed.

[0029] Further preferably, when the deviation value between the fitted spiral line and the modeling boundary is less than 0.5 mm, the spiral lines of the front and rear boundaries of the glass surface of the front door glass can be confirmed.

[0030] Further preferably, the specific steps of step S201 of the glass surface spiral axis are:

[0031] S2011, respectively selecting the upper and lower endpoints and the midpoint of the front and rear boundaries of the shaped glass surface, wherein the point through which the spiral line of the front and rear boundaries of the glass finally determined is passed by default as the midpoint;

[0032] S2012, respectively draw circles with the upper end point, the middle point, and the lower end point on the front boundary and the rear boundary, and find the centers of the two circles on the front and rear boundaries by picking the centers of the circles. The line connecting the two points is the spiral axis O1;

[0033] S2013, then start the second fitting cycle: based on the midpoints of the front and rear boundaries of the modeling and the spiral axis O1, obtain two planes of the front and rear boundaries: project the upper and lower endpoints on the same side of the modeling boundary onto the planes respectively, and obtain new coordinate points;

[0034] S2014, construct a circle with three points based on the new coordinate point and the midpoint, and find the centers of the two circles at the front and rear boundaries by picking the center of the circle. The line connecting the two points is the spiral axis O2;

[0035] S2015, repeat the above steps until the deviation between On and On-1 is less than a preset value, thereby confirming the spiral axis O of the glass surface.

[0036] Still further preferably, in step S2015, when the deviation between On and On-1 is less than 1 mm, the requirement is met.

[0037] Preferably, step S3 includes: extracting the front and rear door window surfaces of the shape, intersecting the fitted front and rear door glass spiral lines with the water section surface respectively to obtain intersection points; making an arc line through three points - the intersection points of each door spiral line and the intersection point adjacent to the door, which is the guide line of the door glass surface.

[0038] Preferably, in step S4, the deviation between the spiral surface and the glass surface is less than 1 mm.

[0039] Preferably, in step S4, the top stop point of the glass is trimmed according to the shape window frame boundary and the window sill line.

[0040] Preferably, in step S5, the rotation angle α of any point A of the door glass around the spiral axis when it descends to the bottom dead point B is determined. The descent of point A along the spiral line to point B is decomposed into ① rotation around the spiral axis A→A'; ② translation along the spiral axis A'→B, and point B is solved by the following formula:

[0041]

[0042] Where: R is the radius of rotation, P is the helix pitch.

[0043] The beneficial effect of the present invention is that the present invention can be implemented through the same design module to realize an integrated design from door glass production to motion verification. When a new shape appears, it is only necessary to replace the corresponding shape reference line, and through parameter association, the new glass surface and glass motion trajectory can be fitted. This method greatly saves design time and verification time while ensuring the quality of the glass fitting surface.

[0044] While accurately fitting the glass spiral surface, the present invention can further simulate the glass surface (upper dead point) and the corresponding lower dead point position when it descends; and the present invention can quickly realize the solution of fitting the glass surface to the upper and lower dead points by replacing the modeling glass boundary line in the CATIA module GSD, which can free itself from the existing complexity and efficiently serve the automobile door design. BRIEF DESCRIPTION OF THE DRAWINGS

[0045] Figure 1 is a system flow chart of the present invention;

[0046] Figure 2 These are the preliminary testing conditions for the shaped glass surface of the present invention;

[0047] Figure 3 It is a fitting schematic diagram of a cycle of the glass axis of the present invention;

[0048] Figure 4 is a schematic diagram of the spiral line of the glass surface of the present invention;

[0049] Figure 5 It is a schematic diagram of trimming the large surface and the top dead center position of the glass of the present invention;

[0050] Figure 6 is a flow chart of the steps for determining the bottom dead point of the glass of the present invention;

[0051] Figure 7 It is a schematic diagram of the decomposition of the bottom stop point movement of the glass surface of the present invention. DETAILED DESCRIPTION

[0052] The technical solution of the present invention (including the preferred technical solution) is further described in detail below by means of the accompanying drawings and by listing some optional embodiments of the present invention. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of the present invention.

[0053] The present invention designs a systematic design method that combines door glass production and motion verification. After the shape is input, the front and rear boundary spiral lines of the glass surface are fitted, and then a glass spiral surface with high precision is produced by determining the guide line; after the spiral surface is confirmed, the glass surface, that is, the upper dead point, and the position of any state corresponding to the glass when it descends are simulated to obtain the position of the lower dead point.

[0054] In another embodiment of the present invention, specifically: after the shape is input, the shape glass surface state that can be fitted with a double helix is ​​first confirmed through a preliminary recognition mechanism, and then the front and rear boundary spiral lines of the glass surface are fitted, and then a glass spiral surface with high precision is produced by determining the guide line. After the spiral surface is confirmed, the glass surface, that is, the upper dead point, and the position of any state corresponding to it when it descends can be simulated under the same design module, and the position of the lower dead point can also be obtained.

[0055] Since the motion trajectory of any point on the glass surface is a spiral line, the present invention decomposes the spiral motion of any point on the glass surface into two steps: first, the rotational motion around the axis, and then the translational motion along the axis. These two steps can be easily implemented in the CATIA General Design Module (GSD), and parametric design verification can be achieved through parameter association.

[0056] like Figure 1 As shown in the figure, firstly, the CAS state is preliminarily judged by the input CAS, which is used as the preliminary screening for the production of high-quality glass surfaces. Then, the spiral lines of the front and rear boundaries of the glass surface are fitted by the CAS that meets the requirements. Then, the guide line of the glass surface is confirmed by 3 points. The glass spiral surface is made by the spiral line and the guide line, and the upper stop point of the glass is trimmed. Finally, according to the principle that the motion trajectory of any point on the glass surface is a spiral line, the lower stop point of the glass is quickly confirmed through parametric design. In this way, any motion position can be obtained.

[0057] Specifically, the systematic design method combining door glass manufacturing and motion verification designed by the present invention includes the following steps:

[0058] S1, modeling input CAS;

[0059] Usually, the glass surface can be made directly by inputting the modeling boundary, but there is no preliminary prediction mechanism in the early stage, and the quality of the glass surface cannot be guaranteed. It needs to be solved repeatedly to fit the glass surface that meets the requirements. At the same time, the production of the glass surface and the motion verification process are generally not implemented through parameterization in the same module, and the whole process is time-consuming.

[0060] In another embodiment of the present invention, Figure 2 As shown, in order to reduce repetition time and improve efficiency, it is necessary to preliminarily judge the CAS status when inputting the shape. Specifically, four condition checks are required to determine whether the shape meets the requirements of high-quality glass surface fitting:

[0061] ① In order to meet the functionality of glass lifting, the curvature radius R1 of the front and rear boundaries of the shaped glass surface must be greater than the pre-judgment value; preferably, the pre-judgment value is 1000mm;

[0062] ② In order to reduce the difficulty of glass manufacturing and the fitting deviation of the subsequent glass original surface, the curvature radius R2 of the window sill sealing strip needs to be greater than the pre-judgment value; preferably, the pre-judgment value is 15000mm;

[0063] ③ To ensure the smoothness of glass lifting, the inclination angle α of the B-pillar window frame should be smaller than the predicted value, and the preferred predicted value is 15°;

[0064] ④ To ensure the normal lifting of the glass, the front and rear boundaries of the glass must be parallel;

[0065] When the glass surface provided by the shape meets the above four conditions, start designing the glass surface.

[0066] S2, fitting the spiral lines of the front and rear boundaries of the glass surface according to CAS;

[0067] Extract the front and rear boundary lines of the front door glass, perform front and rear boundary line fitting, and generate two spiral lines on the front door glass; extract the front and rear boundary lines of the rear door glass, perform front and rear boundary line fitting, and generate two spiral lines on the rear door glass;

[0068] In another embodiment of the present invention, fitting the front and rear boundary spiral lines of the glass surface is described below.

[0069] like Figure 3 and Figure 4As shown in the figure, in the design state, the front and rear glass boundaries are a segment of two helices with equal pitch and coaxiality. Enter the "Generative Surface Design (GSD)" module of CATIA, and use the "Midpoint Method" design method. The specific steps of the basic fitting idea are as follows:

[0070] S201, obtaining the spiral axis of the glass surface according to the upper and lower endpoints and the midpoint of the front and rear boundaries of the glass surface by fitting; the details are as follows:

[0071] S2011, respectively selecting the upper and lower endpoints P1-1, P1-2, P1-3, P1-4 and the midpoints Pm1 and Pm2 of the front and rear boundaries of the shaped glass, wherein the points through which the spiral lines of the front and rear boundaries of the glass finally determined are passed by default as points Pm1 and Pm2;

[0072] S2012, respectively draw circles with the upper end point, the middle point, and the lower end point on the front boundary and the rear boundary, and find the centers Pc1-1 and Pc1-2 of the two circles on the front and rear boundaries by picking the centers of the circles. The line connecting the two points is the spiral axis O1;

[0073] S2013, then start the second fitting cycle, based on the midpoints Pm1 and Pm2 of the front and rear boundaries of the modeling and the spiral axis O1, obtain the two planes PLAN1 and PLAN2 of the front and rear boundaries, where PLAN1 and PLAN2 are the normal planes of O1 passing through Pm1 and Pm2, respectively, project the upper and lower endpoints P1-1 and P1-2 of the modeling boundary to PLAN1, project the upper and lower endpoints P1-3 and P1-4 of the modeling boundary to PLAN2, and obtain new coordinate points P2-1, P2-2, P2-3, and P2-4;

[0074] S2014, according to the new front boundary three-point combination: point P2-1, P2-2, midpoint Pm1, and the rear boundary three-point combination: point P2-3, P2-4, midpoint Pm2, obtain a new circle, repeat the first method of obtaining the O1 axis, that is, the method in step S2012, to obtain a new spiral axis O2;

[0075] S2015, solve the fitting multiple times until the deviation between On and On-1 is less than 1 mm, which meets the requirements, thereby confirming the spiral axis O of the glass surface.

[0076] S202, the front and rear boundary spiral lines are calculated according to the formula based on the glass spiral axis O and the front and rear boundary midpoints Pm1 and Pm2:

[0077]

[0078] Among them, α is the rotation angle, P is the pitch of the spiral line where the point is located, Ri is the distance between the point and the spiral axis, and S is the length of the spiral line motion;

[0079] By adjusting the pitch P value, when the deviation between the fitted spiral line and the modeling boundary is less than 0.5 mm, the front and rear boundary spiral lines CV1 and CV2 of the glass surface of the front door glass can be confirmed.

[0080] According to the above method, the front and rear boundary spiral lines CV3 and CV4 of the glass surface of the rear door glass can be confirmed in the same way.

[0081] S3, confirming the guide lines of each door according to the window surface of each door and the fitted spiral line;

[0082] Extract the front and rear door window surfaces of the modeling, intersect the fitted front and rear door glass spiral lines CV1, CV2, CV3, and CV4 with the water section surface respectively, and obtain the intersection points P1, P2, P3, and P4. In order to take into account the surface difference of the front and rear door glass surfaces at the B-pillar and ensure the appearance perception of the modeling, the guide line of the front door glass surface is made into an arc line CC1 formed by three points P1, P2, and P3; the guide line of the rear door glass surface is made into an arc line CC2 formed by three points P2, P3, and P4, such as Figure 5 shown.

[0083] S4, making high-precision glass spiral surface and trimming the glass top dead center;

[0084] like Figure 5 As shown, the obtained glass spiral line and guide line are used to obtain a high-precision spiral surface, and the spiral surface deviation and glass surface deviation are less than 1mm. Then, the upper stop point of the glass, that is, the surface of the glass in the closed state, is trimmed according to the shape window frame boundary and window sill line.

[0085] S5, decompose the spiral motion of any point on the glass surface into two steps: first, the rotational motion around the axis, and then the translational motion along the axis to determine the bottom dead point position.

[0086] After the glass surface is trimmed to the top dead center position, the spiral motion of any point on the glass surface is decomposed into two steps: first, the rotational motion around the axis, and then the translational motion along the axis to determine the bottom dead center position. Figure 6 and Figure 7 As shown in the figure, the rotation angle α of any point A of the door glass around the spiral axis when it descends to the lower dead point B is determined by the relationship between the lower dead point position of the glass and the Z direction of the door window sill line. The movement of any point A on the glass surface when it descends along the spiral line to B can be regarded as consisting of two sub-movements: ① rotation around the spiral axis A→A'; ② translation along the spiral axis A'→B.

[0087] The trajectory of point A rotating around Orr to A' is an arc, so the relationship between the arc length A A' and the rotation radius R is as follows:

[0088]

[0089] Through the above relationship, the position of A' can be determined. Then, A' is translated to B along the axis O. The relationship between A'B and the helical pitch P is as follows:

[0090]

[0091] Through the above relationship, the position of B can be determined.

[0092] In this way, through parametric design, the spiral motion of any point on the glass surface can be decomposed into two steps: first, the rotational motion around the axis, and then, second, the translational motion along the axis, to determine the bottom dead point position.

[0093] The following describes how to express the two movements ① and ② above in the Generative Surface Design (GSD) module of CATIA:

[0094] (1) Rotation

[0095] In CATIA Generative Surface Design (GSD), select the rotation command and define the mode as "rotation-angle" to rotate the glass around the spiral axis by an angle α;

[0096] (2) Translation

[0097] After completing the rotation command, translate the rotated glass surface. In CATIA Generative Surface Design (GSD), select the translation command, define the vector as "direction-distance", and translate the rotated glass surface by a displacement S along the spiral axis.

[0098] Only through the above two steps, not only can the accurate position of the bottom stop point of the glass surface be determined, but also the position of the glass in any state during movement can be obtained. After fitting the glass surface, this step can be completed synchronously by outputting the corresponding parameters, without the need for complicated DMU, ​​which is easy to operate and greatly improves efficiency.

[0099] The above design process can be implemented through the same design module to achieve an integrated design from door glass production to motion verification. When a new shape appears, it is only necessary to replace the corresponding shape baseline. Through parameter association, the new glass surface and glass motion trajectory can be fitted. This method can greatly save design time and verification time while ensuring the quality of the glass fitting surface.

[0100] While accurately fitting the glass spiral surface, the present invention can further simulate the glass surface (upper dead point) and the corresponding lower dead point position when it descends; and the present invention can quickly realize the solution of fitting the glass surface to the upper and lower dead points by replacing the modeling glass boundary line in the CATIA module GSD, which can free itself from the existing complexity and efficiently serve the automobile door design.

[0101] Those skilled in the art will readily appreciate that the above are merely preferred embodiments of the present invention and are not intended to limit the present invention. Any modifications, combinations, replacements, improvements, etc. made within the spirit and principles of the present invention are included within the protection scope of the present invention.

Claims

1. A systematic design method combining door glass production and motion verification, characterized in that: The following steps are involved: S1, modeling input CAS; S2, fitting the spiral lines of the front and rear boundaries of the glass surface according to CAS; S201, obtaining the spiral axis of the glass surface by fitting the upper and lower endpoints and the midpoint of the front and rear boundaries of the glass surface; S2011, respectively selecting the upper and lower endpoints and the midpoint of the front and rear boundaries of the shaped glass surface, wherein the point through which the spiral line of the front and rear boundaries of the glass finally determined is passed by default as the midpoint; S2012, respectively draw circles with the upper end point, the middle point, and the lower end point on the front boundary and the rear boundary, and find the centers of the two circles on the front and rear boundaries by picking the centers of the circles. The line connecting the two points is the spiral axis O1; S2013, then start the second fitting cycle: based on the midpoints of the front and rear boundaries of the modeling and the spiral axis O1, obtain two planes of the front and rear boundaries: project the upper and lower endpoints on the same side of the modeling boundary onto the planes respectively, and obtain new coordinate points; S2014, construct a circle with three points based on the new coordinate point and the midpoint, and find the centers of the two circles at the front and rear boundaries by picking the center of the circle. The line connecting the two points is the spiral axis O2; S2015, repeat the above steps until the deviation between On and On-1 is less than a preset value, thereby confirming the glass surface spiral axis O; S202, calculating the front and rear boundary spiral lines according to the formula based on the glass spiral axis O and the midpoints of the front and rear boundaries: ； Among them, α is the rotation angle, P is the pitch of the spiral line where the point is located, Ri is the distance between the point and the spiral axis, and S is the length of the spiral line motion; By adjusting the pitch P value, when the deviation value between the fitted spiral line and the modeling boundary meets the preset conditions, the spiral line of the front and rear boundaries of the glass surface can be confirmed; S3, confirming the guide lines of each door according to the window surface of each door and the fitted spiral line; S4, using the obtained glass spiral line and guide line to make a high-precision glass spiral surface and trim the glass top dead point; S5, decompose the spiral motion of any point on the glass surface into two steps: first, the rotational motion around the axis, and then the translational motion along the axis to determine the bottom dead point position.

2. The systematic design method combining door glass manufacturing and motion verification according to claim 1 is characterized by: When inputting the shape, it is necessary to preliminarily judge the CAS status. Specifically, four condition checks are required to determine whether the shape meets the requirements of high-quality glass surface fitting: ① The curvature radius R1 of the front and rear boundaries of the shaped glass surface must be greater than the predicted value; ②The curvature radius R2 of the window sill sealing strip must be greater than the predicted value; ③ The inclination angle α of the B-pillar window frame of the shape must be smaller than the predicted value; ④The front and rear borders of the glass must be parallel; When the glass surface provided by the shape meets the above four conditions, start designing the glass surface.

3. The systematic design method combining door glass manufacturing and motion verification according to claim 2 is characterized by: The predicted value in the above requirement ① is 1000mm; the predicted value in the above requirement ② is 15000mm; the predicted value in the above requirement ③ is 15°.

4. The systematic design method combining door glass manufacturing and motion verification according to claim 1 is characterized in that: In step S202, when the deviation value between the fitted spiral line and the modeling boundary is less than 0.5 mm, the spiral lines of the front and rear boundaries of the glass surface of the front door glass can be confirmed.

5. The systematic design method combining door glass manufacturing and motion verification according to claim 1 is characterized in that: In step S2015, when the deviation between On and On-1 is less than 1 mm, the requirement is met.

6. The systematic design method combining door glass manufacturing and motion verification according to claim 1 is characterized by: Step S3 includes: extracting the front and rear door window surfaces, intersecting the fitted front and rear door glass spiral lines with the water section surface to obtain intersection points; making an arc line through three points - the intersection points of each door spiral line and the intersection point adjacent to the door, which is the guide line of the door glass surface.

7. The systematic design method combining door glass manufacturing and motion verification according to claim 1 is characterized in that: In step S4, the spiral surface deviation and the glass surface deviation are less than 1 mm; the top dead point of the glass is trimmed according to the shape window frame boundary and the window sill line.

8. The systematic design method combining door glass manufacturing and motion verification according to claim 1 is characterized in that: In step S5, the rotation angle α of any point A of the door glass around the spiral axis when it descends to the bottom dead point B is determined. The descent of point A along the spiral line to point B is decomposed into ① rotation around the spiral axis A→A'; ② translation along the spiral axis A'→B. Point B is solved by the following formula: , line segment ; Where: R is the radius of rotation, P is the helix pitch.

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