20.1 - Initial Proposal

Introduction

Soft robotic grippers have gained significant attention due to their ability to interact safely with objects of varying shapes and fragility. Unlike traditional rigid grippers, compliant fingers deform during contact, allowing them to adapt to object geometry and distribute contact forces more effectively. This capability makes them useful for applications such as delicate object manipulation, robotic prosthetics, and human-robot interaction.

However, purely soft mechanisms are difficult to analyze using classical kinematics because their motion arises from distributed material deformation rather than discrete joints. The pseudo-rigid-body (PRB) model provides a practical method for analyzing compliant mechanisms by approximating flexible segments as rigid links connected by torsional spring joints. This allows traditional kinematic analysis techniques to be applied to mechanisms that physically behave as flexible structures.

The motivation of this project is to investigate how PRB modeling can be used to design and predict the motion of a tendon-actuated compliant robotic finger. Understanding this relationship would allow designers to create compliant grippers with predictable motion while maintaining the advantages of soft structures.

Problem Statement

Designing compliant robotic fingers with predictable motion is challenging because the motion of the mechanism is determined by flexible material deformation rather than simple rigid-body rotation.

In a tendon-actuated compliant finger, pulling the tendon produces coordinated bending across multiple flexure joints. The resulting motion depends on multiple interacting factors, including the geometry of the links, the stiffness of the flexure joints, and the routing path of the tendon.

A desired behavior for robotic fingers is sequential curling, where the proximal joints close before distal joints. This motion allows the finger to wrap around objects and increase contact area during grasping. Achieving this coordinated motion requires careful interaction between tendon forces, joint stiffness, and link geometry.

Without a systematic modeling approach, designers must rely on trial-and-error prototyping or computationally expensive finite element simulations to understand how these factors influence finger motion.

This behavior cannot be easily achieved using simple pin joints alone because rigid joints would require multiple actuators or complex linkages to replicate the distributed compliance found in soft mechanisms. However, compliant joints allow force and motion to distribute naturally along the finger structure.

The problem addressed in this project is therefore to determine how actuator input, joint stiffness, and finger geometry influence the motion of a tendon-actuated compliant finger.

Proposed Mechanism

The proposed mechanism is a tendon-driven compliant finger fabricated as a single 3D-printed component using TPU. The finger consists of several rigid segments connected by thin flexure regions that act as compliant joints. These flexure sections allow the finger to bend when actuated while maintaining structural continuity without traditional pin joints.

To analyze the mechanism, the compliant finger will be represented using the pseudo-rigid-body (PRB) method, where the rigid segments are treated as links and the flexure regions are approximated as torsional spring joints.

This representation converts the compliant structure into an equivalent planar three-revolute (3R) kinematic chain, allowing classical kinematic analysis methods to be applied.

Actuation is provided by nylon webbing sewn along the inner (palmar) surface of the TPU finger, which functions as a tendon. The webbing is routed through small guides near each flexure joint and anchored near the fingertip. A servo motor at the base of the finger pulls the webbing, reducing its effective length and causing the joints to rotate sequentially.

The routing geometry of the tendon introduces a constraint that relates motor displacement to the joint angles of the finger.

Two identical fingers will be mounted on a frame to form a planar pinch gripper, with one servo motor actuating each finger. As the tendon is pulled, the compliant joints bend and the finger curls inward, allowing the mechanism to conform to objects and increase contact area during grasping.

Scope of Work

Pseudo-Rigid Body Modeling
a. Develop an equivalent rigid-link representation of the compliant finger and determine torsional stiffness values for each flexure joint based on material properties and geometry.
Kinematic Analysis
a. Model the finger as a planar 3R mechanism and derive the forward kinematics to determine fingertip position as a function of joint angles.
Tendon Constraint Modeling
a. Formulate the relationship between motor displacement and joint angles using the tendon length constraint equation.
Velocity and Acceleration Analysis
a. Differentiate the constraint equations to obtain relationships between actuator motion and joint angular velocities and accelerations.
Prototype Fabrication
a. Fabricate the compliant finger using TPU through 3D printing.
b. Integrate the nylon webbing tendon routing system into the finger structure.
c. Connect the tendon system to a servo actuator to provide tendon actuation.
Experimental Validation
a. Use camera-based motion tracking to measure joint angles and fingertip trajectories during operation.
b. Compare the measured motion with predictions from the pseudo-rigid-body (PRB) model.
The goal of this project is to complete the analytical modeling of the compliant finger, fabricate a working prototype, and experimentally validate the predicted kinematic behavior using motion tracking. The final result will be a functioning prototype and a mathematical model capable of predicting finger motion from actuator input.

Preliminary Design Ideas

Preliminary CAD design for a prototype to be 3D printed has been completed. The entirety of the finger will be printed in flexible TPU. A flexible cloth strip will be run through the slots and fixed to the last linkage. When the cloth is pulled the finger flexes and curls. A variable table below represents the parameters that will be varied to test and validate the kinematics of our model.

Although the physical system is a compliant mechanism, we drafted a few preliminary kinematic diagrams to represent an effective rigid-body model of the finger. The input mechanism consists of a simple slider-pulley system that pulls the tendon responsible for actuating the finger. This input mechanism has one degree of freedom.

For the finger itself, we initially used a simplified kinematic model that allowed us to apply the Grashof equation to analyze the linkage behavior. Because the tendon pull fully determines the finger motion, we expected the mechanism to have one degree of freedom. However, applying the mobility equation to this rigid approximation resulted in a calculated mobility of two degrees of freedom.

This discrepancy arises because the rigid-body model does not account for the compliance of the tendon or the effective torsional spring behavior at the pseudo-joints in the finger. To better represent the physical system, we developed a slider-spring model that includes these compliant effects. While this model no longer allows the direct application of the Grashof equation, it more accurately captures the behavior of the compliant mechanism we are attempting to represent.

Sources

[1] D. Rus and M. T. Tolley, “Design, fabrication and control of soft robots,” Nature, vol. 521, pp. 467–475, 2015.

[2] A. M. Dollar and R. D. Howe, “The highly adaptive SDM hand: Design and performance evaluation,” The International Journal of Robotics Research, vol. 29, no. 5, pp. 585–597, 2010.