CN112560198B - Activity domain subdivision method for measuring human upper limb operation work efficiency - Google Patents

Activity domain subdivision method for measuring human upper limb operation work efficiency Download PDF

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CN112560198B
CN112560198B CN202011517219.0A CN202011517219A CN112560198B CN 112560198 B CN112560198 B CN 112560198B CN 202011517219 A CN202011517219 A CN 202011517219A CN 112560198 B CN112560198 B CN 112560198B
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CN112560198A (en
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杜俊敏
呼慧敏
孙维玉
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Beihang University
China National Institute of Standardization
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China National Institute of Standardization
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Abstract

The invention belongs to the field of human operation work efficiency research, and particularly relates to an activity domain subdivision method for measuring human upper limb operation work efficiency. The invention firstly divides the upper limb movement range on a vertical axis, the range on the vertical axis is from the functional height of the arm lifting vertically to the functional height of the arm drooping naturally, and the hand length is taken as the step length and is divided into a plurality of layers; then, the range of the hand with the maximum extension at a certain height is divided into a left area and a right area by taking the sagittal plane of the right shoulder joint as a boundary, each area comprises one or more circular arcs, and the area units are equally divided on each circular arc. The method can be applied to all areas of the reach of the upper limbs of the human body, including the maximum reach in front of the coronal plane of the human body and the maximum reach behind the coronal plane of the human body.

Description

Activity domain subdivision method for measuring human upper limb operation work efficiency
Technical Field
The invention belongs to the field of human operation work efficiency research, and particularly relates to an activity domain subdivision method for measuring human upper limb operation work efficiency.
Background
The operation safety, efficiency and comfort of the operation device depend on the position and layout of the operation device to a great extent, when the position and layout of the operation device are not appropriate, not only can misoperation increase and efficiency is low, but also an operator can be tired, and even joint diseases are caused by accumulation.
In order to determine the reasonable position and layout of the manual control device in the design process of the human-computer interface or to evaluate the position and layout rationality of the manual control device in the ergonomics evaluation of the existing human-computer interface, the operating ergonomics of the upper limbs of the human body in the motion field need to be mastered. In the experiment of measuring the operation efficiency of the upper limbs of the human body, the position of the control device has direct influence on the measurement result. From the perspective of the human upper limb performing the operation, i.e. the specific position of the upper limb, especially the hand position, in the upper limb activity domain, has a direct impact on the manipulation ergonomics.
At present, the division of human upper limb activity areas in the hand movement industry at home and abroad is mainly based on the division of a horizontal plane of an operation table and a sagittal plane of a human body. For example, the upper limb movement range on the horizontal plane of the console is obtained from the body size calculation (see fig. 1), or divided on the basis of angle in combination with the visual reachable domain in the sagittal and horizontal planes of the body (see fig. 2). These methods accomplish ergonomic layout design and evaluation of manual manipulators using rough area division, but as the number of manipulators increases, such rough area division methods result in insufficient precision and reduced support for layout design and evaluation of manipulators.
For example, when the layout design of a display control device in an aircraft cockpit is studied, because the number of instrument switches, display screens and control devices to be arranged is huge, devices with a small difference in importance or use frequency are often lost due to rough area division. If the upper limb activity field cannot be effectively subdivided, the layout ergonomics of the cockpit device and the pilot operation are greatly influenced.
Disclosure of Invention
The method mainly aims at the defect that the precision of the existing upper limb activity domain dividing method is insufficient when the operation work efficiency is measured, and the defect can cause that a large number of control devices cannot obtain an accurate operation work efficiency value when the human-computer interface layout is designed and evaluated, and the reliability of upper limb operation work efficiency analysis can be greatly influenced due to the lack of the precision of the part. The invention mainly aims at the activity domain of the upper limb of the human body and realizes the approximate equivalent division of the activity domain by a subdivision method. Particularly, the invention introduces the upper limb structure and the size data of the human body, subdivides the upper limb activity area in each level of horizontal plane based on the maximum reachable area of the upper limb, stretches the subdivision boundary of the plane area in the vertical direction, and completes the subdivision of the upper limb activity area, thereby avoiding the precision problem caused by rough division of the activity area and finally obtaining the operation work efficiency experimental result with precise positioning.
In order to achieve the above object, the present invention provides an activity domain subdivision method for measuring human upper limb operation ergonomics, which is characterized by comprising the steps of:
step 1: acquiring human body size data comprising arm function length H and hand length A;
step 2: dividing the upper limb activity domain on the vertical axis based on the acquired human body size data, wherein the specific process is as follows:
step 2-1: calculating the range of the motion domain of the upper limb on the vertical axis, wherein S = H1-H2=2H, H1 is the function height of the arm lifted vertically, and H2 is the function height of the arm which naturally drops;
step 2-2: taking the multiple d of the hand length A as a step length, calculating the number n of layers and the number m of layers required to be divided in the moving domain range S, wherein n = [2H/d × A +0.5], and m = n +1;
step 2-3: calculating the height L of each layer based on the calculated active domain range S and the number n of layers, wherein L =2H/n;
step 2-4: determining the heights of the layers from top to bottom by taking the layer height L as a step length;
and 3, step 3: dividing the plane of the maximum reachable region of the upper limb on each layer of the front m-1 layer into a left region and a right region by taking the sagittal plane of the right shoulder peak point as a boundary, establishing one or more layers of circular arcs in the left region and the right region, and equally dividing each layer of circular arcs to obtain one or more region units;
and 4, step 4: and (4) calculating the obtained position coordinates of each area unit by taking the projection point O of the right shoulder peak point on each layer as a coordinate origin.
Further, the specific process of step 3 is as follows:
step 3-1: recording the projection of the sagittal plane of the right shoulder peak point on each layer from 1 st to m-1 st as the y axis, and recording the projection point R right in front of the projection point O of the right shoulder peak point on each layer i Taking k points a as starting points in sequence along the y-axis 1 ,a 2 ,…,a k-1 ,a k Wherein R is i I =1,2, \ 8230;, m-1, projection length of arm functional length on the ith height level, R i a 1 ＝a 1 a 2 ＝…＝a k-1 a k ＝L，a k O＜L；
Step 3-2: dividing left region
By OR i Is diameter, per O and R i Two points draw a circle, and the semicircular arc on the left side of the y axis is marked as arc L 0, which is the outermost arc of the left region; with a of 1 a k Is diameter, through a 1 And a k Two points draw a circle, and the semicircular arc on the left side of the y axis is marked as arc L 1; with a 2 a k-1 Is diameter, through a 2 And a k-1 Two points draw a circle, and the semicircular arc on the left side of the y axis is marked as arc L 2, the same can be done in sequence to form a circular arc L j, j =1,2, \8230, t, t = k/2, k is an even number; t = (k-1)/2, k is odd; t +1 closed graphs are formed between adjacent arcs and the y axis, namely the left side area is divided into a t +1 part;
step 3-3: dividing the right region
Taking a projection point O of the right shoulder peak point on each layer as a circle center, and taking a point R right in front of the projection point O i Draw a circle for the radius, and denote the arc of the quarter circle on the right side of the y-axis as arc R 0, which is the outermost arc of the right region; using O point as the center of circle and Oa as the center of circle k Draw a circle for the radius, and denote the arc of the quarter circle on the right side of the y-axis as arc R j ', j' =1,2, \ 8230;, k; k +1 closed graphs are formed between adjacent arcs and the y axis, namely the right side area is divided into a k +1 part;
step 3-4: equally dividing the outermost layer of circular arcs to obtain a plurality of area units; the specific process is as follows:
circular arc in left region L 0 and the circular arc in the right region R 0, forming a continuous curve cur0, and rounding the ratio of the arc length of the curve cur0 to the layer height L to obtain the number of segments n cur0 By the number of segments n cur0 A curve cur0 is averaged to obtain n on the curve cur0 cur0 -1 segmentation point; the circular arc to be located in the left region L The segmentation points on 0 are respectively connected with the circle centers of the left areas, and the connection lines are connected with the circular arcs arc L 0、arc L 1 collectively forming a region unit; the circular arc to be located in the right region R The segment points on 0 are respectively connected with the circle centers of the right regions, and the connection lines are connected with the circular arcs arc R 0、arc R 1 collectively forming a plurality of area units;
step 3-5: the circular arc in the left region is equally divided L j, obtaining one or more region units; the specific process is as follows:
to arc L The ratio of the arc length of j to the layer height L is rounded to obtain an arc L Number of segments n of j arcLj By the number of segments n arcLj Equipartition arc L j, in the arc L N is obtained at j arcLj 1 segmentation point and connecting the segmentation point with the circle center of the left area, wherein the connecting lines and two adjacent circular arcs form an area unit;
when the number of segments n arcLj Equal to 1, representing a circular arc L j is not required to be segmented, and arc L The region composed of j and the y axis is merged into a region unit in the right region adjacent to the region;
step 3-6: divide the arc in the right region equally R j', obtaining a plurality of region units; the specific process is as follows:
to arc R The ratio of the arc length of j' to the layer height L is rounded to obtain an arc R Number of segments n of j arcRj’ By the number of segments n arcRj’ Equally divide the arc R j' on the arc R N is obtained at j arcRj’ 1 segmentation point and connecting the segmentation point with the circle center of the right area, wherein the connecting lines and two adjacent arcs as well as the x axis and the y axis form a plurality of area units;
when the number of segments n arcRj’ Equal to 1, representing a circular arc R j' without segmentation, arc R The region j' composed with the x-axis and the y-axis merges into a region unit in the left region adjacent thereto.
The invention has the beneficial effects that: the invention subdivides the upper limb movement domain, ensures the rigor and the accuracy of the operation work efficiency measurement, and provides a precise data base for the subsequent operation work efficiency evaluation or the human-computer interface design; the invention can also be used for positioning and optimizing the layout of the space position of the manual control device, and ensures that the control device is reasonably arranged and is positioned at the proper position in the upper limb moving area.
Drawings
Fig. 1 is a schematic diagram of the division of the upper limb movement range based on the horizontal plane of the operation table in the prior art;
FIG. 2 is a diagram illustrating the division of the range of motion of the upper limb based on angle in the prior art, wherein (a) is in the sagittal plane of the human body and (b) is in the horizontal plane;
FIG. 3 is a flow chart of an activity domain subdivision method for measuring human upper limb operation ergonomics according to an embodiment of the present invention;
FIG. 4 is a schematic diagram of the division of the P95 male upper limb activity zone on the vertical axis according to the embodiment of the present invention;
FIG. 5 is a schematic diagram illustrating the division of the area unit of layer (2) according to an embodiment of the present invention;
fig. 6 is a schematic diagram illustrating the division of the area units in the (1) th to (7) th layers according to the embodiment of the present invention.
Detailed Description
The present invention is further described below in conjunction with the drawings and the embodiments, it is to be understood that the embodiments described below are intended to facilitate the understanding of the present invention and do not have any limiting effect thereon.
In this embodiment, the maximum reachable region in front of the coronal plane of the human body is subdivided into two regions, as shown in fig. 3, which specifically includes the following steps:
step 1: acquiring human body size data;
applicable national standards and other documents, such as GB10000-88 adult size, can be consulted, or actual measurement can be carried out on a testee as required to obtain the human body size data, including arm function length H, hand length A and the like. The area subdivision range of the embodiment covers 360 degrees of the area around the human body in an all-around mode, and the range on the vertical axis is from the arm to the functional height of the arm which naturally hangs down. It should be understood that the functional length of the arm as referred to herein refers to the vertical distance from the acromion point to the centerline of the fist-grasping axis when the upper limb naturally sags when holding a cylindrical rod with a diameter of 20 mm; the functional height of the arm for lifting vertically and the arm for drooping naturally refers to the vertical distance from the shoulder peak point to the central axis of the cylindrical rod when the cylindrical rod with the diameter of 20mm is held by a hand. In addition, the upper limbs and arms in the present invention are two expressions of a term.
Step 2: dividing an upper limb activity domain on a vertical axis based on the acquired human body size data; the specific process is as follows:
step 2-1: holding a cylindrical rod with the diameter of 20mm by hand, vertically lifting the arm, and recording the height from the ground of the center line of the fist holding shaft at the moment as H1; holding a cylindrical rod with the diameter of 20mm by hand, naturally dropping the arm, and recording the height above the ground of the center line of the fist holding shaft as H2; the interval H1 to H2 is denoted as the range of the upper limb in the vertical axis, and specifically, H1-H2 is 2 times the arm function length H, i.e., 2h =h1-H2.
Step 2-2: taking the hand length a as a reference value, calculating and rounding the number of layers n required to be divided to obtain the range of the motion field of the upper limb on the vertical axis, i.e. n = [2H/a +0.5], and adding 0.5 is adopted in the text for rounding. In practice, if finer layer division is required (corresponding to more layers), the hand length a may be replaced by a certain ratio of the hand length a (e.g. 1/2, 1/3, etc. of the hand length a) as required, and n is obtained by calculating the rounding.
Step 2-3: after the number of layers n is calculated, the number of layers n is divided by 2H to obtain the height L of each layer, i.e., L =2H/n.
Step 2-4: determining the height of each layer according to the calculated layer height L:
the height of each layer can be accurately determined by utilizing the measuring plate, the measuring plate of the highest layer is firstly placed, the measuring plate is horizontally placed, the height of the measuring plate is H1, then each layer of height L is used as a step length, the height value of each layer of measuring plate is obtained, and then each layer of height is obtained.
Advantageously, in the experimental part related to the layer height placement of the measuring plate, the body size of the testee is not limited, the placement height of the measuring plate is independently calculated according to the body size of each testee, and the height of the measuring plate is placed according to the calculated layer height value. Because the height H1 and the height L of the highest layer of measuring plate are divided according to the arm function length H and the hand length A of each tested person, the height of each layer of measuring plate belongs to individual setting and is changed along with the human body size of each tested person. The invention can eliminate the unfair size problem caused by equidistant measurement, although the adjusting time in the experiment is increased.
In this embodiment, for example, for a P95 male (the size is from the 95 th percentile male size in GB 10000-88), the ratio of the double arm function length to the hand length is about 7, so that the number of layers n is 7 and the number of layers m is 8 in the vertical axis direction. As shown in fig. 4, circles (1) - (8) on the left side in the figure are layer numbers, (1) represents that the hand function is high when the arm is lifted up in the sitting posture, and (8) represents that the hand function is high when the arm naturally droops in the sitting posture, namely, the ranges (1) - (8) are the hand function reachable ranges. The hand function here is a hand function of a full hand grip gesture, i.e., a hand function gesture with the smallest reachable range. The numbers beside the layer numbers (1) - (8) are the height of each layer of measuring plate from the ground, the numbers on the right sides of the 7 layer grids are the sizes of various indexes, including sitting posture eye height, sitting posture shoulder height, sitting posture elbow height, sitting posture thigh height, sitting posture wrist height and shank adding height, and the number units in the figures are all mm. The scale size of each finger in the figure comes from the national standard GB10000-88 adult human body size, and is taken as an application example of the invention. In practical application, researchers can measure the size of a subject by themselves according to needs to obtain the data, and the data of GB10000-88 can be adopted.
And 3, step 3: dividing and calculating the left and right side areas of the sagittal plane of the right shoulder joint
Based on the division of the upper limb movement range on the vertical axis in step 2, the present embodiment subdivides the region in front of the coronal plane. Dividing the plane of the maximum reachable region of the upper limb on any height layer from the (1) th layer to the (7) th layer into a left part and a right part by taking the sagittal plane of the right shoulder peak point as a boundary, wherein the left area is marked as an area I, and the right area is marked as an area II. And establishing a plurality of layers of circular arcs in each area, and obtaining area units by equally dividing the arc length of each circle of circular arc. In the present embodiment, the area block of the layer (2) is taken as an example, and as shown in fig. 5, the projection point O of the right shoulder peak point on the layer height is taken as the front R 2 Starting at a point and segmenting inward (toward projection point O) in units of the layer height, where R 2 The projection length of the functional length of the arm on the height layer, and the ratio of the projection length to the height of the height layer is the total number M of the segments that can be divided by the segment, namely M = [ R2/L +0.5]]. According to such a segmentation approach, the line segment OR can be shown in FIG. 5 2 2 segmentation points and 2 end points, such as the segmentation points in fig. 5Is a 1 And a 2 The endpoints are respectively: and the right shoulder peak point O and the projection point O of the right shoulder peak point on the layer height are right in front of the point R2.
The partitioning of the two regions, region I and region II, in fig. 5 is further described below.
For the block of the region I, the projection point O on the layer height from the right shoulder peak point is right in front of R 2 Starting at point, first take a distance L of layer height along the y-axis inward (i.e. toward the right shoulder peak), and record it as a 1 Point, then point a 1 Is continued to take a distance of layer height L along the y-axis, and is marked as a 2 And (4) point. With r = OR 2 The diameter is determined, the y axis is taken as the central line, a circle is drawn through the point of the shoulder peak of the right shoulder, and the semicircular arc on the left side of the y axis is marked as arc L 0; the layer height L is taken as the diameter, i.e. the layer height of a 1 And a 2 Two points draw a circle, and the semicircular arc on the left side of the y axis is marked as arc L 1. Arc L 0、arc L The 1 and y axes constitute two closed figures, i.e. the area I is divided into two parts, as shown in fig. 5.
For the block of the region II, the O point is taken as the center of a circle, and R is taken as the center of a circle 2 Draw a circle for the radius, and denote the arc of the quarter circle on the right side of the y-axis as arc R 0; using O point as the center of circle and Oa as the center of circle 1 Draw a circle for the radius, and denote the arc of the quarter circle on the right side of the y-axis as arc R 1; using O point as the center of circle and Oa as the center of circle 2 Draw a circle for the radius, and denote the arc of the quarter circle on the right side of the y-axis as arc R 2. Arc R 0、arc R 1、arc R The 2 and x-axis, y-axis form three closed figures, i.e. the area II is divided into three parts.
The outermost arcs in zone I and zone II, i.e. the arc in zone I L 0 and arc in region II R 0, forming a continuous curve cur0. The ratio of the arc length of curve cur0 to the layer height L is rounded to obtain the number of segments n cur0 The curve cur0 is divided equally by the number of segments, on which curve n is obtained cur0 -1 segmentation point. The segment points in the area I are respectively connected with the circle center of the area I, the segment points in the area II are respectively connected with the circle center of the area II, and the connecting lines are connected with the circle center of the area I and the circle center of the area IIArc L 0、arc L 1 together with the circular arc in the region II R 0、arc R 1 together form the area units 2, 3, 4, 5, 6 in fig. 5.
Then, in the region II, the arc is aligned R 1, the ratio of the arc length to the layer height L is rounded to obtain the arc R 1, by which the arc is equally divided R 1, obtaining a plurality of block points, and connecting lines of the block points and the circle center of the area II and the circular arc R 1、arc R 2 together form the area units 7, 8 in fig. 5.
Then in the region I, to the arc L 1, the ratio of the arc length to the layer height L is rounded to obtain the arc L The number of segments of 1 equals 1, meaning that the arc need not be segmented, arc L The region consisting of 1 and the y-axis merges into the adjacent region unit 7 in region II.
Then, the arc is aligned in the same way R 2 by segmentation, to circular arc R 2, the ratio of the arc length to the layer height L is rounded to be equal to 1, which means that the arc does not need to be segmented, and arc R The region consisting of 2 and the x-axis and the y-axis is merged into the adjacent region unit 2 in the region I.
For the stratification of other heights, the blocking method of the outermost layer arc is the same as that of the curve cur0 described above, the blocks of each layer of circular arcs from outside to inside are all equal to the circular arc L 1、arc R 1、arc R The blocking method of 2 is the same. According to the above-mentioned blocking method, the upper limb activity field of the present embodiment can be subdivided into 59 area units with approximately equal volume, as shown in fig. 6, fig. (a) - (g) are schematic diagrams of the area units of the present embodiment from the (1) th layer to the (7) th layer from top to bottom, respectively, and the spatial area unit is drawn downward from each layer, i.e. the spatial area unit is located below the layer height, for example, the spatial area unit of the (1) th layer is located between the (1) th layer and the (2) th layer, so the (8) th layer has no spatial area unit. Further, on the (1) th layer, OR 1 Is 0. This layer is provided because when the palm of a person is open for operation (e.g., pressing a button with a forefinger), there is an operating range, and the range No. 1 drawn on the layer (1) (shown in FIG. (a)) is schematically indicatedThe range of the palm when open, the diameter of the semicircle drawn in the figure is equal to the length from the palm center to the middle finger tip.
And 4, step 4: obtaining active domain subdivision results
Based on the above region unit dividing method, the projection point O of the right shoulder peak point on the layer height is used as the origin of coordinates, and the position coordinates of each region unit are calculated. There are three main types of position coordinates: the unit coordinates of the region passing through the sagittal plane of the right shoulder peak point (i.e., point R in FIG. 5) 2 、a 1 、a 2 The coordinates of the right shoulder peak point), the coordinates of the left area unit of the sagittal plane where the right shoulder peak point is located (the coordinates of the block points in the area I), and the coordinates of the right area unit of the sagittal plane where the right shoulder peak point is located (the coordinates of the block points in the area II). After all the area unit coordinates are obtained, the method can be used for an experimental site, and the position coordinates of 59 area units are automatically generated according to the human body size of a testee.
In this embodiment, the region in front of the human coronal plane is described, and for the subdivision of the region in back of the human coronal plane, the coronal plane may be used as the center, and the region in front of the coronal plane is mirror-symmetrically mapped, so that the region in back of the coronal plane can be obtained. In practice, for controller operation in the region behind the coronal plane, access to the body by rotation may be required.
It will be apparent to those skilled in the art that various modifications and improvements may be made to the embodiments of the present invention without departing from the inventive concept thereof.

Claims (2)

1. An activity domain subdivision method for measuring human upper limb operation work efficiency is characterized by comprising the following steps:
step 1: acquiring human body size data comprising arm function length H and hand length A;
step 2: dividing the upper limb activity domain on the vertical axis based on the acquired human body size data, wherein the specific process is as follows:
step 2-1: calculating the range S = H1-H2=2H of the range of the motion area of the upper limb on the vertical axis, wherein H1 is the functional height of the arm lifted vertically, and H2 is the functional height of the arm drooping naturally;
step 2-2: taking the multiple d of the hand length A as a step length, calculating the number n of layers and the number m of layers required to be divided in the active domain range S, wherein n = [2H/d A +0.5], and m = n +1;
step 2-3: calculating the height L of each layer based on the calculated active domain range S and the number n of layers, wherein L =2H/n;
step 2-4: determining the heights of the layers from top to bottom by taking the layer height L as a step length;
and 3, step 3: dividing the plane of the maximum reachable region of the upper limb on each layer of the front m-1 layer into a left region and a right region by taking the sagittal plane of the right shoulder peak point as a boundary, establishing one or more layers of circular arcs in the left region and the right region, and equally dividing each layer of circular arcs to obtain one or more region units;
and 4, step 4: taking a projection point O of the right shoulder peak point on each layer as a coordinate origin, and calculating the obtained position coordinates of each area unit;
the functional length of the arm refers to the vertical distance from the acromion point to the centre line of the fist holding axis when the user holds a cylindrical rod with the diameter of 20mm and naturally drops the upper limb; the functional height of the arm for lifting vertically and the arm for drooping naturally refers to the vertical distance from the shoulder peak point to the ground when a cylindrical rod with the diameter of 20mm is held by a hand.
2. The method according to claim 1, wherein the specific process of step 3 is as follows:
step 3-1: recording the projection of the sagittal plane of the right shoulder crest point on each layer from 1 st to m-1 st as the y axis, and recording the projection from the right shoulder crest point on each layer as the point R right in front of the projection point O i Taking k points a along the y axis 1 ,a 2 ,…,a k-1 ,a k Wherein R is i I =1,2, \ 8230;, m-1, projection length of arm functional length on the ith height level, R i a 1 ＝a 1 a 2 ＝…＝a k-1 a k ＝L，a k O＜L；
Step 3-2: dividing left region
By OR i Is the diameter, O and R i Two points draw a circle, draw yThe semicircular arc on the left side of the shaft is denoted as arc L 0, which is the outermost arc of the left region; with a of 1 a k Is diameter, through a 1 And a k Two points draw a circle, and the semicircular arc on the left side of the y axis is marked as arc L 1; with a of 2 a k-1 Is diameter, through a 2 And a k-1 Two points draw a circle, and the semicircular arc on the left side of the y axis is marked as arc L 2, repeating the above steps to form a circular arc L j, j =1,2, \8230, t, t = k/2, k is an even number; t = (k-1)/2, k is odd; t +1 closed graphs are formed between adjacent arcs and the y axis, namely the left side area is divided into a t +1 part;
step 3-3: dividing the right region
Taking a projection point O of the right shoulder peak point on each layer as a circle center, and taking a point R right in front of the projection point O i To draw a circle for the radius, the arc of the quarter circle on the right side of the y-axis is denoted as arc R 0, which is the outermost arc of the right region; using O point as the center of circle and Oa as the center of circle k To draw a circle for the radius, the arc of the quarter circle on the right side of the y-axis is denoted as arc R j ', j' =1,2, \8230k; k +1 closed graphs are formed between adjacent arcs and the y axis, namely the right side area is divided into a k +1 part;
step 3-4: equally dividing the outermost layer of arc to obtain a plurality of area units; the specific process is as follows:
circular arc in left region L 0 and the circular arc in the right region R 0, forming a continuous curve cur0, and rounding the ratio of the arc length of the curve cur0 to the layer height L to obtain the number of segments n cur0 By the number of segments n cur0 A curve cur0 is averaged to obtain n on the curve cur0 cur0 -1 segmentation point; the circular arc to be located in the left region L The segmentation points on 0 are respectively connected with the circle centers of the left areas, and the connection lines are connected with the circular arcs arc L 0、arc L 1 collectively form a region unit; the circular arc to be located in the right region R The segment points on 0 are respectively connected with the circle centers of the right regions, and the connection lines are connected with the circular arcs arc R 0、arc R 1 collectively forming a plurality of area units;
step 3-5: the circular arc in the left region is equally divided L j, obtaining one or more region units; the specific process is as follows:
to arc L The ratio of the arc length of j to the layer height L is rounded to obtain an arc L Number of segments n of j arcLj By the number of segments n arcLj Equally divide the arc L j, in the arc L N is obtained at j arcLj 1 segmentation point and connecting the segmentation point with the circle center of the left area, wherein the connecting lines and two adjacent circular arcs form an area unit;
when the number of segments n arcLj Equal to 1, representing a circular arc L j need not be segmented, and arc L The region composed of j and the y axis is merged into a region unit in the right region adjacent to the region;
step 3-6: divide the arc in the right region equally R j', obtaining a plurality of region units; the specific process is as follows:
to arc R The ratio of the arc length of j' to the layer height L is rounded to obtain an arc R Number of segments n of j arcRj’ By the number of segments n arcRj’ Equally divide the arc R j' on the arc R N is obtained at j arcRj’ 1 segmentation point is connected with the circle center of the right area through lines, and the lines and two adjacent circular arcs as well as the x axis and the y axis form a plurality of area units together;
when the number of segments n arcRj’ Equal to 1, representing a circular arc R j' need not be segmented, and arc R The region j' composed with the x-axis and the y-axis merges into a region unit in the left region adjacent thereto.
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