Table of Contents:
Introduction
Linkage 1 Analysis
2.3 Acceleration Analysis
Linkage 2 Analysis
3.3 Acceleration Analysis
Linkage 3 Analysis
1. Introduction
This section presents the kinematic analysis used to describe the motion of the proposed finger exoskeleton mechanism. The analysis is developed to relate the input motion of the linkage to the resulting joint configuration and overall finger motion. Position, velocity, and acceleration relationships are established so that the mechanism can be evaluated in terms of motion transmission, smoothness, and feasibility for guided finger flexion.
Desmos Project: 
Offset Inversion 2 Four-Bar Slider CrankPreview
The design of this project is heavily inspired by the UT Hand Exoskeleton papers.
Figure 1. UT Hand Exoskeleton inspiration image showing three separate four-bars which helps to control finger motion. Linkage are labeled in accordance to the analysis.
2. Linkage 1 Analysis
2.1 Position Analysis
Figure 2. Position analysis setup and vector-loop formulation for the slider-block offset inversion mechanism.
Figure 3. Continued position analysis showing the solution for the remaining positional variables.
Figure 4. Motion profile of the first linkage showing the 90 degree range of motion of link 4 (magenta link).
Figure 5. Requirement Met: Theta 4 should be nearly linear and have a range over 90 degrees.
Figure 6. Requirement Met: L4 should be relatively smooth and have a range less than 21mm
2.2 Velocity Analysis
Figure 7. Velocity analysis obtained by differentiating the vector-loop equations.
Figure 8. Velocity Analysis cont.
Figure 9. Motion profile of first linkage with velocity vectors.
Figure 10. Requirement Met: Mechanical advantage (input at theta 2, output at theta 4) should be reasonable (i.e., greater than 1 for power, less than 3 for safety).
Figure 11. Requirement Met: All velocities should be smooth and within reason (i.e., less than 15 rad/sec or mm/sec).
Figure 12. Requirement Met: All velocities should be smooth and within reason (i.e., less than 15 rad/sec or mm/sec).
Figure 13. Requirement Met: All velocities should be smooth and within reason (i.e., less than 15 rad/sec or mm/sec).
2.3 Acceleration Analysis
Figure 14. Initial acceleration analysis derived from the differentiated velocity relations.
Figure 15. Final acceleration relations for the mechanism.
Figure 16. Motion profile of first linkage with tangential & normal acceleration component vectors.
Figure 17. Motion profile of first linkage with acceleration vectors.
Figure 18. Requirement Met: All accelerations should be smooth and within reason (i.e., less than 15 rad/sec^2).
Figure 19. Requirement Met: All accelerations should be smooth and within reason (i.e., less than 15 rad/sec^2).
Figure 20. Requirement Met: All accelerations should be smooth and within reason (i.e., less than 15 rad/sec^2).
3. Linkage 2 Analysis
3.1 Position Analysis
Figure 21. Motion profile of second linkage. Requirement Met: Point O8, Point D, and Point E (bottom three joints) should be able to be nearly collinear (means PIP finger joint can bend 90 degrees).
3.2 Velocity Analysis
Figure 22. Motion profile of the second linkage with velocity vectors.
Figure 23. Requirement Met: Mechanical advantage (input at theta 6, output at theta 8) should be reasonable (i.e., greater than 1 for power, less than 3 for safety).
Figure 24. Requirement Met: All velocities should be smooth and within reason (i.e., less than 15 rad/sec).
3.3 Acceleration Analysis
Figure 25. Motion profile of second linkage with acceleration vectors.
Figure 26. Requirement Met: All accelerations should be smooth.
4. Linkage 3 Analysis
Linkage 3 is not powered as it will only be use to properly mount the mechanism to the finger. Thus, no velocity of acceleration analysis was needed for this linkage. Since linkage 3 is Grashof (see below), it will be able to conform to any DIP angle as needed, thus strict position analysis is not necessary.
