Here is a Python function to generate test cases for the "Twirl Around" problem statement:

```python
import random

def generate_dataset():
    # Length of the bar (1.0 ≤ L ≤ 500.0)
    L = round(random.uniform(1.0, 500.0), 6)
    
    # Rotations (1.0 ≤ R ≤ 10.0)
    R = round(random.uniform(1.0, 10.0), 6)
    
    # Number of vertices (3 ≤ N ≤ 100)
    N = random.randint(3, 100)
    
    # Generate vertices (Xi, Yi) for the polygon
    vertices = []
    
    # Ensure the first vertex meets the condition X1 ≤ -1, Y1 = 0
    first_vertex = (random.randint(-1000, -1), 0)
    vertices.append(first_vertex)
    
    # Ensure the second vertex meets the condition X2 ≥ 1, Y2 = 0
    second_vertex = (random.randint(1, 1000), 0)
    vertices.append(second_vertex)
    
    # Generate the remaining vertices
    for _ in range(N - 2):
        x = random.randint(-1000, 1000)
        y = random.randint(-1000, 1000)
        vertices.append((x, y))
    
    # Ensure the vertices are in counter-clockwise order (convex polygon)
    vertices = sorted(vertices, key=lambda v: (v[1], v[0]))
    
    # Format dataset as a string
    dataset = f"{L} {R} {N}\n"
    for vertex in vertices:
        dataset += f"{vertex[0]} {vertex[1]}\n"
    
    return dataset

def tcgen():
    # Number of datasets (up to 100)
    num_datasets = random.randint(1, 100)
    
    # Generate datasets
    datasets = [generate_dataset() for _ in range(num_datasets)]
    
    # Add the end of input indicator "0 0 0"
    datasets.append("0 0 0\n")
    
    # Join datasets into a single string
    input_data = ''.join(datasets)
    
    return input_data

# Example usage
if __name__ == "__main__":
    print(tcgen())
```

This code generates a random test case for the "Twirl Around" problem, ensuring that the conditions specified for the input are met. Each dataset includes the length of the bar \(L\), the number of rotations \(R\), and the vertices of the polygon. The function `tcgen()` generates up to 100 such datasets and appends the end-of-input indicator "0 0 0" at the end.