2. If the arc R60 is tangent to the circle 40, the distance between its center and the center of the circle 40 must be 20+60=80.
3. Draw an auxiliary circle with the diameter of 160(2x80) with the center 40 as the center, and then you can determine that the center of arc R60 is on this circle.
4. Another tangent condition is that the arc R60 is also tangent to the auxiliary line 15, so it can be determined that the horizontal distance from the center of the arc R60 to the auxiliary line 15 is 60. Draw such an auxiliary line.
5. In this way, the center of the arc R60 can be determined, which is at the intersection of the newly drawn auxiliary line 60 and the auxiliary circle with the diameter of 160 drawn in Figure 3. The position indicated by the red X in the picture.
6. Draw an arc with a radius of 60 with the newly determined point as the center, and finish.
7. The second step is to determine the arc R40. Draw a few auxiliary elements first. It is important to draw an arc with a radius of 48, that is, a part of the outer circle of the hook, which is 9 to the right of the circle 40 in the first step.
8. The reason is the same as before. If the arcs R40 and R48 are tangent, the distance between the centers of the arcs R40 and R48 is 40+48=88. Draw an auxiliary circle with a diameter of 176(2x88) around the center of R48. It is certain that the center of arc R40 is on this auxiliary circle.
9. Draw another auxiliary line 15, which is located on the right side of the center of the hook inner circle 40. Another tangent condition is that the arc R40 is also tangent to the newly drawn auxiliary line, so the horizontal distance from the center of the arc R40 to the auxiliary line 15 is 40. Draw an auxiliary line like this.
10. The intersection of auxiliary circle 176 and auxiliary line 40 is the center of arc R40. The position indicated by the red X in the picture.
1 1.Arc R40 has been completed.
12. Remove unnecessary auxiliary lines and complete two arcs.
13. Next, determine the arc R40 tangent to the inner circle of the hook tip. Draw an auxiliary line below the center of the inner circle 40 with a distance of 15. According to the known conditions, the center of arc R40 is on this auxiliary line, so the distance between the center of arc R40 and the center of inner circle 40 is 40+20=60.
14. Draw an auxiliary circle with a diameter of 120(2x60) with the center of the inner circle 40 as the center. It is certain that the center of arc R40 is on this circle. The intersection of auxiliary circle 120 and auxiliary line 15 is the center of arc R40.
15. Next, determine the arc R23 outside the hook tip. It is known that arc R23 is tangent to arc R48. Then, according to the above steps, draw a circle with the diameter of 142(2x(23+48)) with the center of arc R48 as the center, and you can determine the center of arc R23 on this auxiliary circle.
16. It is known that the center of arc R23 and the center of arc R48 are on the same horizontal line. Then the intersection of this horizontal line and the auxiliary circle 142 is the center of the arc R23.
17. Finally, determine the arc R4 on the hook tip. Given that R4 and R23 are tangent, the distance between the center of R4 and the center of R23 is 4+23=27.
In addition, R4 and R40 are inscribed, so the distance between the two centers is 40-4=36.
18. Draw the first auxiliary circle with the center of R23 as the center, the center of R4 must be on this circle, and draw the second auxiliary circle with the center of R40 as the center, with a diameter of 72(2x36), and the center of R4 must also be on this circle. So the intersection of these two auxiliary circles is the center of R4. The position indicated by the red X in the picture.
19. Draw an arc R4. It's done.
In fact, the most important point of this diagram is to find the center of the arc. According to the known tangency condition, it is not difficult to draw more auxiliary circles by subtracting the inscribed radius and adding the circumscribed radius.