Code Explanation in Python

The provided code snippet is written in Python and performs calculations related to geometric angles using trigonometry. Specifically, it is likely aimed at determining the angles necessary for robotic arm movements based on specified parameters.

Code Breakdown

Step 1: Importing Libraries

import math

• This line imports the math module, which contains useful mathematical functions and constants to perform operations such as square roots and trigonometric calculations.

Step 2: Declaring Constants

base_radius = 75
bicep_length = 120
forearm_length = 315
end_effector_radius = 60

• These variables represent fixed parameters in the scenario:
  • base_radius: The radius at the base of a structure.
  • bicep_length: The length of the bicep segment of a robotic arm.
  • forearm_length: The length of the forearm segment.
  • end_effector_radius: The radius of the tool or gripper at the end of the arm.

Step 3: Defining Points in 3D Space

x = 50
y = 50
z = 100

• Here, x, y, and z denote the coordinates of a point in 3D space where the arm is expected to reach. This information is critical for calculating the required angles.

Step 4: Calculating Distances and Angles

h = z + end_effector_radius
r = math.sqrt(x**2 + y**2)

• h: Represents the vertical distance from the base to the target point. It combines the z coordinate with the end_effector_radius.
• r: Calculates the horizontal distance from the vertical axis to the target point using the Pythagorean theorem.

Step 5: Computing Angles

angle_a = math.atan2(y, x) - math.acos((bicep_length**2 - forearm_length**2 - r**2) / (-2 * forearm_length * r))
angle_b = math.atan2(y, x) + math.acos((bicep_length**2 - forearm_length**2 - r**2) / (-2 * forearm_length * r))
angle_c = math.atan2(h, r) - math.acos((bicep_length**2 - forearm_length**2 - h**2) / (-2 * forearm_length * h))

• math.atan2(y, x): This function computes the angle in radians between the x-axis and the line connecting the origin to the point (x, y). It accounts for the signs of both coordinates to determine the correct quadrant.
• Angle Calculations:
  • angle_a: Represents one joint angle involving the bicep and forearm lengths, adjusted by the computed angle from the attached point to (x, y).
  • angle_b: Similar to angle_a, but it adds instead of subtracts the angle from the atan2 function. This computation accounts for the possible two configurations of the arm.
  • angle_c: This angle involves the vertical height h with respect to r, factoring in the bicep and forearm lengths.

Step 6: Printing the Results

print(angle_a)  
print(angle_b)  
print(angle_c)

• Finally, this section outputs the calculated angles angle_a, angle_b, and angle_c to the console. These angles can be used to control the actuators in a robotic arm mechanism.

Key Concepts Explained

• Trigonometry: The use of trigonometric functions such as atan2 and acos is fundamental in robotic kinematics to determine angles from coordinate positions.
• Pythagorean Theorem: This theorem determines distances in coordinate geometry, applied here to find the horizontal distance r.
• Inverse Kinematics: The overall objective appears to be related to inverse kinematics, where the goal is to calculate joint positions given a desired end effector position.

Alternative Example for Angle Calculation

To further illustrate the angle calculations, consider this alternative approach for angle determination for a point at (x, y):

def calculate_angle(x, y, arm_length):
    r = math.sqrt(x**2 + y**2)
    angle = math.atan2(y, x)
    if r <= arm_length:  # Ensures the target is within reach
        return angle
    else:
        return None  # Target out of reach

• This function calculates the angle for a specified arm length and checks if the point is within reach.

By breaking down the original code into its components, the understanding of the robotic arm's angle calculations is simplified, making it more accessible to learners. For deeper exploration of concepts such as trigonometry and robotics, consider utilizing the Enterprise DNA Platform.