Prosthetic Thumb Kinematics Visualization

Project Overview

This project simulates and visualizes the kinematics of a prosthetic thumb mechanism. The thumb is modeled as a 4-bar linkage (BCDE) with an additional triangular linkage (DEF) to define a point of interest, F. The simulation explores the range of motion of this mechanism in both 2D and 3D space.

• The 2D simulation (show.py) analyzes the motion of the 4-bar linkage in a single plane, driven by an angle theta_drive.
• The 3D visualization (visualize_thumb_3d.py) extends this by placing the 2D linkage in a 3D global coordinate system. It introduces a second degree of freedom, theta_A, which rotates the entire 2D linkage plane around the global Y-axis. The script then calculates and visualizes the 3D workspace of point F and shows snapshots of the linkage in various configurations.

The global origin (0,0,0) is considered to be at a point 'A'. The 2D linkage's reference point 'B' is positioned relative to 'A' by a fixed vector. The theta_A rotation occurs around the global Y-axis passing through 'A'.

Files

• show.py:

  • Simulates the 2D kinematics of the 4-bar linkage (BCDE) and the extended point F.
  • Calculates the positions of all joints for a range of theta_drive angles (0° to -30°).
  • Plots the trajectories of points B, D, and F.
  • Displays snapshots of the linkage configuration at various theta_drive angles.

• visualize_thumb_3d.py:

  • Takes the 2D linkage model from show.py.
  • Introduces a global coordinate system with origin A.
  • Defines the initial position of point B relative to A (VEC_A_to_B).
  • Simulates two degrees of freedom:
    1. theta_drive: Internal angle of the 4-bar linkage (0° to -30°).
    2. theta_A: Rotation of the 2D linkage plane around the global Y-axis (0° to -90°).
  • Calculates the 3D coordinates of all joints (B, C, D, E, F) for a grid of theta_A and theta_drive angles.
  • Prints the 3D coordinates of the joints for 5 specific snapshot configurations.
  • Generates a 3D plot showing:
    • The global origin A.
    • The workspace of point F as a continuous surface.
    • Snapshots of the complete 3D linkage at the 5 specified configurations.

• Reference Images (Conceptual - Not part of the codebase execution but provide context for the mechanism design):

  • Angles4Bar.jpg (Assumed to define linkage parameters and fixed angles used in show.py)
  • 2D-1DOF-ThumbFullRangeOfMotion.jpg (Assumed to illustrate the 2D motion simulated by show.py)

Prerequisites

• Python 3.x
• The following Python libraries:
  • numpy
  • matplotlib
  • scipy

You can install these libraries using pip:

pip install numpy matplotlib scipy

How to Run

1. 2D Simulation (show.py): To run the 2D simulation and see the planar motion of the linkage:

   python show.py

   This will generate two plots: one showing the trajectories of points B, D, and F, and another showing snapshots of the linkage.

2. 3D Visualization (visualize_thumb_3d.py): To run the 3D visualization and see the workspace of point F and 3D linkage snapshots:

   python visualize_thumb_3d.py

   This will first print the 3D coordinates of the joints for 5 specific configurations to the console. Then, it will display a 3D plot showing the workspace of point F as a surface, the linkage snapshots, and the global origin A.

Key Features

• 2D Kinematic Solver: Utilizes scipy.optimize.least_squares to solve the loop closure equations for the 4-bar linkage.
• Parametric Motion: Simulates motion based on one (in 2D) or two (in 3D) driving angles.
• Trajectory Plotting: Visualizes the path of key points in 2D.
• Linkage Snapshots: Shows the configuration of the entire linkage at specific angle increments in both 2D and 3D.
• 3D Workspace Generation: Calculates the reachable space for point F under two degrees of freedom.
• Surface Visualization: Plots the 3D workspace of point F as a continuous surface.
• Coordinate Transformation: Transforms 2D linkage coordinates into a 3D global frame with rotation.

Mechanism Details

• Core Linkage: A 4-bar planar linkage consisting of points B, C, D, and E.
  • Link lengths: L_CB, L_EB, L_ED, L_CD.
  • Fixed angles: Theta_CB (angle of link CB relative to a fixed direction in the 2D plane), Lambda (angle within link EB).
• Extended Point: Point F is defined by a triangular linkage DEF with fixed lengths L_FD and L_FE.
• Degrees of Freedom (for 3D visualization):
  1. theta_drive (internal to the 2D linkage): Controls the angle of the input link for the 4-bar mechanism. Ranges from 0° to -30°.
  2. theta_A (global rotation): Rotates the plane containing the 2D linkage around the global Y-axis. Ranges from 0° to -90°.
• Global Frame: Point A is at the origin (0,0,0). Point B is initially offset from A by VEC_A_to_B = [-67.597, 51.149, 3.122] mm before any theta_A rotation.