skip to main content
US FlagAn official website of the United States government
dot gov icon
Official websites use .gov
A .gov website belongs to an official government organization in the United States.
https lock icon
Secure .gov websites use HTTPS
A lock ( lock ) or https:// means you've safely connected to the .gov website. Share sensitive information only on official, secure websites.


Title: Design and Modeling of Compliant Four-Bar Mechanisms With Variable Stiffness Links for Multi-Output Trajectory
Abstract This research presents a novel design of a four-bar mechanism featuring a variable stiffness link (VSL) as the output component, aimed at enabling diverse end-effector trajectories without modifying the link length or moment input. By employing both single-beam and multi-section beam configurations within a large deflection model, the study investigates the effect of varying link stiffness under constant load and geometric conditions on the mechanism’s trajectory outcomes. The proposed design was validated through both numerical modeling and experimental testing of a built prototype. The findings confirm the prototype’s alignment with theoretical predictions, highlighting the VSL’s key role in significantly enhancing the adaptability and application range of four-bar mechanisms. This advancement circumvents the traditional constraints of fixed-trajectory mechanisms, proposing a versatile, efficient, and cost-effective solution for complex motion applications in compliant mechanism design.  more » « less
Award ID(s):
2131711
PAR ID:
10635540
Author(s) / Creator(s):
; ; ; ;
Publisher / Repository:
American Society of Mechanical Engineers
Date Published:
ISBN:
978-0-7918-8841-4
Format(s):
Medium: X
Location:
Washington, DC, USA
Sponsoring Org:
National Science Foundation
More Like this
  1. In this study, a novel human-in-the-loop design method using a genetic algorithm (GA) is presented to design a low-cost and easy-to-use four-bar linkage medical device for upper limb muscle rehabilitation. The four-bar linkage can generate a variety of coupler point trajectories by using different link lengths. For this medical device, patients grab the coupler point handle and rotate the arm along the designed coupler point trajectory to exercise upper limb muscles. The design procedures include three basic steps: First, for a set of link lengths, a complete coupler point trajectory is generated from four-bar linkage kinematics; second, optimization-based motion prediction is utilized to predict arm motion (joint angle profiles) subjected to hand grasping and joint angle limit constraints; third, the predicted joint angles and given hand forces are imported into an OpenSim musculoskeletal arm model to calculate the muscle forces and activations by using the OpenSim static optimization. In the GA optimization formulation, the design variables are the four-bar link lengths. The objective function is to maximize a specific muscle’s exertion for a complete arm rotation. Finally, different four-bar configurations are designed for different muscle strength exercises. The proposed human-in-the-loop design approach successfully integrates GA with linkage kinematics, arm motion prediction, and OpenSim static optimization for four-bar linkage design for upper limb muscle strength rehabilitation. 
    more » « less
  2. Abstract This paper introduces a novel matrix-based approach for the simultaneous type and dimensional synthesis of planar four-bar linkage mechanisms, accommodating various practical constraints, including position, velocity, acceleration, and joint placements. Traditional design processes segregate type synthesis, the determination of joint and link configurations, from dimensional synthesis, which involves specifying link sizes and pivot locations. This segregation often leads to complexities in addressing the complete design challenge. The novel methodology proposed in this paper departs from the conventional sequential design approach by concurrently evaluating type and dimensional parameters using a data-driven matrix formulation. The crux of the paper’s methodology involves formulating a singular design equation through a transformation matrix, parameterized by the Cartesian parameters of the mechanism’s dyads. This formulation linearly expresses a broad range of constraints, facilitating the identification of viable solutions through singular value decomposition and null space analysis. This integrated approach not only simplifies the synthesis process but also provides direct insights into the mechanism’s parameters, encompassing both type and dimensions, thereby obviating the need for further interpretative steps common to the use of quaternions and kinematic mapping. In essence, the paper presents two main contributions: the development of a unified design equation capable of encompassing a wide array of constraints within the mechanism synthesis process, and the introduction of an algorithm that effectively identifies all potential planar four-bar linkage mechanisms by accurately satisfying up to five constraints. This approach promises to enhance the design and optimization of mechanical systems by offering a more holistic and efficient pathway to mechanism synthesis. 
    more » « less
  3. Abstract Variable stiffness manipulators balance the trade-off between manipulation performance needing high stiffness and safe human-robot interaction desiring low stiffness. Variable stiffness compliant links provide a solution to enable this flexible manipulation function in human-robot co-working scenarios. In this paper, we propose a novel variable stiffness link based on discrete variable stiffness units (DSUs). A DSU is a parallel guided beam that can adjust stiffness discretely by changing the cross-sectional area properties of the hollow beam segments. The variable stiffness link (named Tri-DSU) consists of three tandem DSUs to achieve eight stiffness modes and a maximum stiffness change ratio of 31. To optimize the design, stiffness analysis of the DSU and Tri-DSU under various configurations and forces was performed by a derived theoretical model compared with finite element analysis (FEA). The analytical stiffness model is derived using the approach of serially connected beams and superposition combinations. It works not only for thin-walled flexure beams but also for general thick beam models. 3-D printed prototypes were built to verify the feature and performance of the Tri-DSU in comparison with the FEA and analytical model results. It’s demonstrated that our analytical model can accurately predict the stiffnesses of the DSU and Tri-DSU within a certain range of parameters. The developed variable stiffness link method and analytical model are extendable to multiple DSUs with different sizes and parameter configurations to achieve modularization and customization. The advantages of the stiffness change mechanism are rapid actuation, simple structure, and compact layout. These methods and results provide a new conceptual and theoretical basis for the development of new reconfigurable cobot manipulators, variable stiffness structures, and compliant mechanisms. 
    more » « less
  4. This paper details the mechanical design and control of a human safety robotic arm with variable stiffness, starting from conceptual design to prototype. The mechanism designed is based on parallel guided beam with a roller slider actuated by a power screw and a DC motor with an encoder for position feedback. Unlike conventional robotic systems that control the stiffness in joints, this design introduces compliance to the robotic arm link itself. By controlling the slider position, the effective length of the link can be adjusted to provide the necessary stiffness change. A PID position controller is employed and the position accuracy is experimentally evaluated. The stiffness variation of the prototype is validated by experiments and FEA simulation. The overall stiffness change achieved is 20-fold. 
    more » « less
  5. Abstract This article introduces a novel methodology based on conditional β-variational autoencoder (cβ-VAE) architecture to generate diverse types of planar four-bar mechanisms for a given coupler curve. Central to our contribution is the novel integration of cross- and self-attention layers within the VAE framework, facilitating an encoding and decoding process that captures the complex interdependencies of mechanism parameters and associated coupler curves. We propose a unified representation scheme for four-bar mechanisms with both revolute and prismatic joints, utilizing a consistent set of joints to describe each mechanism type. To support and validate our methodology, we have compiled an extensive dataset featuring both open and closed coupler curves of the aforementioned mechanism types. Furthermore, the article introduces three metrics aimed at quantifying the efficacy of our model, alongside an innovative algorithm designed to enhance the predictive outcomes by identifying and computing cognate mechanisms. 
    more » « less