Cam Angle Calculation with Polynomial 3

Mechanical Cam angle calculation with length input using polynomial 3 with numpy polyfit

Formula

Angle = (a * Length^3) + (b * Length^2) + (c * Length) + d)

Calculation

Python code for calculating the coefficients a, b, c, and d

import pandas as pd
import numpy as np
import argparse
import sys

def calculate_coefficients(file_name):
    """
    Calculates the coefficients a, b, c, and d for the cubic formula:
    Angle = a * Length^3 + b * Length^2 + c * Length + d

    The script explicitly selects columns by index to handle CSV formatting issues.
    """
    try:
        # Print status messages to stderr (ensures they appear even if stdout is redirected)
        print(f"--- Attempting to process file: {file_name} ---", file=sys.stderr)

        # 1. Load the CSV. header=2 is used to position the header row.
        df = pd.read_csv(file_name, header=2)

        # 2. Select the third and fourth columns (index 1 and 2), which contain Angle and Length.
        df_clean = df.iloc[:, [1, 2]].copy()

        # 3. Explicitly rename columns. Based on the data, the column at index 1 is Angle (0, 2, 4...)
        # and index 2 is Length (0.00, 0.01, 0.06...).
        df_clean.columns = ['Angle', 'Length']

        # Continue with cleaning
        df_clean = df_clean.dropna()

        if df_clean.empty:
            raise ValueError("Data frame is empty after reading or cleaning (check file contents/columns).")

        # Define independent (x) and dependent (y) variables
        # Length is the independent variable (X), Angle is the dependent (Y)
        x = df_clean['Length']
        y = df_clean['Angle']

        # Perform a degree 3 polynomial fit (cubic)
        # polyfit returns coefficients in order of highest power to lowest: (a, b, c, d)
        coefficients = np.polyfit(x, y, 3)
        a, b, c, d = coefficients

        # --- Output the final results to standard output (stdout) ---
        print("\n--- Final Cubic Polynomial Regression Coefficients ---")
        print(f"Model: Angle = (a * Length^3) + (b * Length^2) + (c * Length) + d")
        print(f"a (Length^3 coefficient): {a}")
        print(f"b (Length^2 coefficient): {b}")
        print(f"c (Length^1 coefficient): {c}")
        print(f"d (Constant term): {d}")

    except FileNotFoundError:
        print(f"\nERROR: File not found. Check the path and file name: {file_name}", file=sys.stderr)
    except KeyError as e:
        # This should no longer happen with the .iloc fix, but kept for general robustness
        print(f"\nERROR: Column names 'Angle' or 'Length' not found. KeyError: {e}", file=sys.stderr)
    except ValueError as e:
        print(f"\nERROR: Data processing issue: {e}", file=sys.stderr)
    except Exception as e:
        print(f"\nAn unexpected error occurred during calculation: {e}", file=sys.stderr)


if __name__ == '__main__':
    # Set up argument parser to read the -file_name flag
    parser = argparse.ArgumentParser(description="Calculate cubic polynomial coefficients for Angle vs. Length data.")
    parser.add_argument('-file_name', type=str, required=True, help='The path to the CSV file containing Angle and Length data.')

    args = parser.parse_args()

    calculate_coefficients(args.file_name)

Save this as cam.py.

Cam Data

Save the known cam angle to length data in a csv file names values.csv.

Index	Angle	Length
0	0	0
1	2	0.01
2	4	0.06
3	6	0.16
4	8	0.29
5	10	0.46

Needs these values for every 2 degs and up to 180 which is equivalent to full linear motion length.

Run

Run the code with the following

python3 .\cam.py -file_name values.csv

Output should be

--- Attempting to process file: .\values.csv ---

--- Final Cubic Polynomial Regression Coefficients ---
Model: Angle = (a * Length^3) + (b * Length^2) + (c * Length) + d
a (Length^3 coefficient): 0.0006656070500861079
b (Length^2 coefficient): -0.07551855711975415
c (Length^1 coefficient): 4.172569761404579
d (Constant term): 11.128975872807523

Now, Download the function block library file here and import from Project > Library > Show References and import the library. Fill the values in the function block.