21 fill in the blank 8 points\ndetermine the following dimensions for the given bolt circle if the holes are…

Explanation:

Step1: Assume number of holes

Let's assume there are 6 holes equally - spaced around the bolt - circle. The central angle between each hole is $\theta=\frac{360^{\circ}}{6}=60^{\circ}$.

Step2: Calculate A

If the radius of the bolt - circle is $r = 190$ mm. For the horizontal distance $A$ from the center to the first hole, assuming the first hole is at an angle of $0^{\circ}$ from the horizontal, and using trigonometry in a right - triangle formed with the center of the circle, the radius as the hypotenuse, and the horizontal and vertical distances as the legs. If we consider the right - triangle, and assume the first hole is at an angle $\alpha = 0^{\circ}$ from the horizontal, then $A=r\cos(0^{\circ})$. Since $\cos(0^{\circ}) = 1$, $A = 190\times1=190.0000$ mm.

Step3: Calculate B

For the horizontal distance $B$ to the second hole (at an angle $\alpha = 60^{\circ}$ from the horizontal), using the formula $x = r\cos\alpha$, where $r = 190$ mm and $\alpha = 60^{\circ}$, and $\cos(60^{\circ})=\frac{1}{2}$. So $B = 190\times\cos(60^{\circ})=190\times0.5 = 95.0000$ mm.

Step4: Calculate X

For the vertical distance $X$ to the third hole (at an angle $\alpha = 120^{\circ}$ from the horizontal), using the formula $y = r\sin\alpha$, where $r = 190$ mm and $\alpha = 120^{\circ}$, and $\sin(120^{\circ})=\frac{\sqrt{3}}{2}\approx0.8660$. So $X = 190\times\sin(120^{\circ})\approx190\times0.8660 = 164.5497$ mm.

Step5: Calculate Y

For the vertical distance $Y$ to the second hole (at an angle $\alpha = 60^{\circ}$ from the horizontal), using the formula $y = r\sin\alpha$, where $r = 190$ mm and $\alpha = 60^{\circ}$, and $\sin(60^{\circ})=\frac{\sqrt{3}}{2}\approx0.8660$. So $Y = 190\times\sin(60^{\circ})\approx190\times0.8660 = 164.5497$ mm.

Answer:

(a) $A = 190.0000$ mm (b) $B = 95.0000$ mm (c) $X = 164.5497$ mm (d) $Y = 164.5497$ mm