20. Conjugation of a circular arc and a straight line by a second arc

Here two cases can be considered: external conjugation (Fig. 35, a) and internal (Fig. 35, b). In either case, when constructing a conjugating arc of radius R, the center of conjugation O lies at the intersection of the geometric locations of points equally distant from the straight line and the arc of radius R by the value R ₁ .

When constructing an external mate parallel to a given straight line at a distance R ₁ in the direction of the circle, an auxiliary line is drawn, and from the center O with a radius equal to R + R ₁ , an auxiliary circle, and at their intersection a point O ₁ is obtained - the center of the conjugating circle. From this center of radius R , a conjugating arc is conducted between points A and A ₁ , the construction of which is visible from the drawing.

Fig. 34

Fig. 35

The construction of internal conjugation is characterized in that from the center O an auxiliary arc is carried out with a radius equal to R - R ₁ .