Subtopic: Hitch systems and hitching of tillage implements
Question Statement:
In a tractor three-point linkage operating in the vertical plane, the upper link (top link) slopes downwards towards the implement at an angle of $10^\circ$ to the horizontal, while the lower links slope upwards towards the implement at an angle of $15^\circ$ to the horizontal. Both links converge forward. If the vertical distance between the tractor top link hitch pin and lower link hitch pins is $h = 450\text{ mm}$, the horizontal distance from the tractor hitch pin plane to the virtual hitch point in $\text{m}$ is ________ (round off to 2 decimal places).
Answer Key:
1.01
Step-by-Step Solution & Explanation
Let $X$ be the horizontal distance forward to the intersection of the link centerlines (virtual hitch point):
$X \tan(10^\circ) + X \tan(15^\circ) = h = 0.450\text{ m}$
Given $\tan(10^\circ) \approx 0.17633$ and $\tan(15^\circ) \approx 0.26795$:
$X (0.17633 + 0.26795) = 0.450$
$X (0.44428) = 0.450$
$X = \frac{0.450}{0.44428} \approx 1.0128\text{ m} \approx 1.01\text{ m}$