4.2 - Project Prototype

Table of Contents:

1. Kinematic Analysis

2. Initial Prototype

1. Kinematic Analysis

1.1 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.

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Figure 0. UT Hand Exoskeleton inspiration image showing three separate four-bars which helps to control finger motion. Linkage are labeled in accordance to the analysis.

1.2 Linkage 1 Analysis

1.2.1 Position Analysis

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Figure 1. Position analysis setup and vector-loop formulation for the slider-block offset inversion mechanism.

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Figure 2. Continued position analysis showing the solution for the remaining positional variables.

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Figure 3. Motion profile of the first linkage showing the 90 degree range of motion of link 4 (magenta link).

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Figure 4. Requirement Met: Theta 4 should be nearly linear and have a range over 90 degrees.

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Figure 5. Requirement Met: L4 should be relatively smooth and have a range less than 21mm

1.2.2 Velocity Analysis

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Figure 6. Velocity analysis obtained by differentiating the vector-loop equations.

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Figure 7. Velocity Analysis cont.

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Figure 8. Motion profile of first linkage with velocity vectors.

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Figure 9. 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).

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Figure 10. Requirement Met: All velocities should be smooth and within reason (i.e., less than 15 rad/sec or mm/sec).

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Figure 11. Requirement Met: All velocities should be smooth and within reason (i.e., less than 15 rad/sec or mm/sec).

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Figure 12. Requirement Met: All velocities should be smooth and within reason (i.e., less than 15 rad/sec or mm/sec).

1.2.3 Acceleration Analysis

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Figure 13. Initial acceleration analysis derived from the differentiated velocity relations.

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Figure 14. Final acceleration relations for the mechanism.

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Figure 15. Motion profile of first linkage with tangential & normal acceleration component vectors.

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Figure 16. Motion profile of first linkage with acceleration vectors.

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Figure 17. Requirement Met: All accelerations should be smooth and within reason (i.e., less than 15 rad/sec^2).

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Figure 18. Requirement Met: All accelerations should be smooth and within reason (i.e., less than 15 rad/sec^2).

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Figure 19. Requirement Met: All accelerations should be smooth and within reason (i.e., less than 15 rad/sec^2).

1.3 Linkage 2 Analysis

1.3.1 Position Analysis

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Figure 20. 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).

1.3.2 Velocity Analysis

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Figure 21. Motion profile of the second linkage with velocity vectors.

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Figure 22. 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).

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Figure 23. Requirement Met: All velocities should be smooth and within reason (i.e., less than 15 rad/sec).

1.3.3 Acceleration Analysis

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Figure 24. Motion profile of second linkage with acceleration vectors.

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Figure 25. Requirement Met: All accelerations should be smooth.

1.4 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.

2. Initial Prototype

2.1 Initial CAD

Open Fig 1. Planar view of the finger mechanism showing the MCP, PIP, and DIP linkages. Open Fig 2. Isometric view of the assembled prototype showing linkage structure.	Open Fig 3. Another isometric view highlighting the joint configuration.

Open Fig 1. Planar view of the finger mechanism showing the MCP, PIP, and DIP linkages. Open Fig 2. Isometric view of the assembled prototype showing linkage structure.	Open Fig 3. Another isometric view highlighting the joint configuration.

The finger design is made up of a series of interconnected four-bar linkages stacked from the base of the finger to the tip. Here's how each section is organized:

• Base / Ground: The anchor block at the base, where the motors are housed.

• MCP Linkage (Driven): The first joint assembly, driven by the MCP motor angle. Made up of links L1r to L4r.

• PIP Linkage (Driven): The middle joint assembly, driven by the PIP motor angle. Made up of links L1b to L4b.

• DIP Linkage (Passive): The outermost joint assembly is not directly driven by a motor. Made up of links L1g to L4g.

• Finger Pads: Contact points at the tip that interface with the user's finger

2.2 Kinematic Parameters

The key geometric and actuation limits that define how the exoskeleton moves are summarized in Table 1.

[1] Tower Pro. MG996R High Torque Metal Gear Dual Ball Bearing Servo — Datasheet. Tower Pro Pte. Ltd. Available at: towerpro.com.tw and Amazon

2.3 Kinematic & Mobility Analysis

The system is controlled by two motor inputs (θMCP and θPIP), which together determine the (x, y) position of the fingertip. Each linkage stage is solved using standard four-bar loop-closure equations.

Motion passes through the joints in sequence:

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(1)

The DIP joint has no motor of its own, meaning its angle is fully determined by the position of the PIP joint before it. To confirm the system has the right number of controllable degrees of freedom, the Kutzbach criterion for planar mechanisms is applied:

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(2)

For a single four-bar linkage stage: N = 4, J₁ = 4, J₂ = 0, giving M = 1 (one degree of freedom). Across the full system:

• MCP linkage: 1 actuated DOF

• PIP linkage: 1 actuated DOF

• DIP linkage: 0 actuated DOF (passive - constrained by geometry)

This gives the system exactly 2 Degrees of Freedom in total.

2.4 Motion Profile & Force Analysis

The design produces a curling motion suited for gripping objects. The finger begins bending at the MCP joint, followed by the PIP joint, with the DIP joint passively following along, resulting in a natural inward curl.

The torque produced by the MCP and PIP motors is transferred through the rigid linkages to the fingertip. The force delivered at the tip depends on the geometry of the linkage at any given position, and can be estimated as:

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(3)

where τ is the motor torque and r_eff​ is the effective moment arm.

Based on the selected motors and linkage geometry, the fingertip is expected to produce approximately 10 to 20 N of force, consistent with values reported in prior work [2], [3].

2.5 Prototype Fabrication

The initial prototype was built to demonstrate finger-curling motion and confirm that the compact design is mechanically viable.

• Structural parts were 3D printed using PLA or PETG filament.

• Joints were secured with standard M3 screws and steel pins.

• Servo motors will be mounted at the base (MCP) and along the finger (PIP) to allow testing and control adjustments.

[2] Bützer, T., Lambercy, O., Arata, J., and Gassert, R. RELab tenoexo: A wearable, kinematic compliant, tendon-driven hand exoskeleton for daily life grasping assistance. IEEE Robotics and Automation Letters, 6(2), 1066–1073, 2020.

[3] Polygerinos, P., Wang, Z., Overvelde, J. T., Galloway, K. C., Wood, R. J., Walsh, C. J., and Morel, J. M. Soft robotic glove for combined assistance and at-home rehabilitation. Robotics and Autonomous Systems, 73, 135–143, 2015.

2.6 Iterations and Initial Prototype

These early designs focused on turning basic ideas into something wearable. The goal was to balance how much the fingers can move (range of motion) with keeping the structure stable.

Linkage Design:
The design progressed from simple single joints to multi-link mechanisms. This allowed the device to better match the natural curved motion of a finger instead of a single hinge rotation.

Fit and Comfort:
Straps and finger loops were added to test how well the exoskeleton moves with the hand. This also helped identify pressure points and areas that could restrict motion.

Mechanical Issues:

• Jamming: Some 3D-printed parts interfered with each other, limiting full range of motion.

• Stability: Adding more links reduced stiffness, leading to unwanted twisting in the structure.

Testing Functionality:
These prototypes showed that the actuator can move the fingers as intended without the mechanism failing or collapsing.

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Fig 4. Iterations 1 through 4 of the prototype.

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Open	This iteration showed the need for more clearance around the main pivot point, and it helped identify spacing issues early so future designs can be improved.
Open	This design improved the range of motion and better matched natural finger movement, even though some links still collide.
Open	This design followed a more natural curved motion and helped show where friction needs to be reduced.
Open	This design helped show that using lighter and more flexible parts could be useful for reducing weight, even though it needs more stiffness.

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These images show the prototype’s range of motion during flexion and extension. The multi-link mechanism replicates natural finger curvature and couples motion across the MCP, PIP, and DIP joints.

The results validate the concept, but misalignment and binding indicate the need for refinement to improve smoothness and to maximize ROM.