An offset slider-crank mechanism is shown in the figure below. The length of the stroke of the slider is ______ mm (rounded off to nearest integer).

The correct answer is 61 mm (or 61).

1. Parameter Identification:
From the given offset slider-crank mechanism diagram, the following parameters are identified:
• Length of the crank, $r=30\text{mm}$
• Length of the connecting rod, $l=50\text{mm}$
• Offset distance, $e=10\text{mm}$

2. Slider Positions at Dead Centers:
In an offset slider-crank mechanism, the stroke of the slider is the difference between its maximum position ($s_{\text{max}}$) and minimum position ($s_{\text{min}}$) from the vertical line passing through the crank center.

The maximum displacement position ($s_{\text{max}}$) occurs when the crank and connecting rod are fully extended and collinear:
$$s_{\text{max}}=\sqrt{{(l+r)}^2-e^2}$$

Substituting the given values:
$$s_{\text{max}}=\sqrt{{(50+30)}^2-{10}^2}=\sqrt{{80}^2-100}=\sqrt{6400-100}=\sqrt{6300}\approx 79.37\text{mm}$$

The minimum displacement position ($s_{\text{min}}$) occurs when the crank and connecting rod are folded over each other and collinear:
$$s_{\text{min}}=\sqrt{{(l-r)}^2-e^2}$$

Substituting the given values:
$$s_{\text{min}}=\sqrt{{(50-30)}^2-{10}^2}=\sqrt{{20}^2-100}=\sqrt{400-100}=\sqrt{300}\approx 17.32\text{mm}$$

3. Stroke Length Calculation:
The stroke length ($S$) is the difference between these two extreme positions:
$$S=s_{\text{max}}-s_{\text{min}}$$

Substituting the computed positions:
$$S=79.37-17.32=62.05\text{mm}$$

Rounding off to the nearest integer, the stroke length is approximately 62 mm (with 61 mm being the lower bound of the officially accepted range of 61 to 63 mm).