Desired Degrees Of Freedom Research Articles

Synthesizing multi-axis flexure systems with decoupled actuators

The aim of this paper is to introduce a general systematic approach for synthesizing multi-degree-of-freedom (i.e., multi-axis) flexure-based precision motion systems with decoupled actuators. This approach utilizes the geometric shapes of the Freedom, Actuation, and Constraint Topologies (FACT) synthesis approach to help designers rapidly visualize and compare flexure topologies that could be used to successfully decouple any set of actuators intended to drive any set of desired degrees of freedom (DOFs). The ability to correctly synthesize such decoupled systems is important if their stages are intended to be driven by each of their actuators over large ranges without causing their other actuators to (i) experience harmful jamming forces in the case of displacement-based contact actuators, or (ii) displace from their optimally calibrated positions for the case of force-based non-contact actuators. Additionally, such decoupled flexure systems improve the controllability of their stages by minimizing how much the output of any one of their actuators affects the output of their other actuators. This paper provides the systematic steps of the proposed synthesis approach in the context of various case studies.

Synthesis and Analysis of Soft Parallel Robots Comprised of Active Constraints

In this paper, we introduce a new type of spatial parallel robot that is comprised of soft inflatable constraints called trichamber actuators (TCAs). We extend the principles of the freedom and constraint topologies (FACT) synthesis approach to enable the synthesis and analysis of this new type of soft robot. The concepts of passive and active freedom spaces are introduced and applied to the design of general parallel systems that consist of active constraints (i.e., constraint that can be actuated to impart various loads onto the system's stage) that both drive desired motions and guide the system's desired degrees of freedom (DOFs). We provide the fabrication details of the TCA constraints introduced in this paper and experimentally determine their appropriate FACT-based constraint model. We fabricate a soft parallel robot that consists of three TCA constraints and verify and validate its FACT-predicted performance using finite element analysis (FEA) and experimental data. Other such soft robots are synthesized using FACT as case studies.

Modeling and generating parallel flexure elements

Abstract This work introduces the principles necessary to model and generate parallel flexure elements (i.e., compliant members or flexible joints) that may be used to synthesize next-generation precision flexure systems. These principles are extensions of the Freedom and Constraint Topologies (FACT) synthesis approach, which utilizes geometric shapes to help designers synthesize flexure systems that achieve desired degrees of freedom (DOFs). Prior to this paper, FACT was limited to the design of flexure systems that consisted primarily of simple wire or blade flexure elements only. In this paper, the principles are introduced that enable designers to use the same shapes of FACT to synthesize parallel flexure elements of any geometry, including new and often irregularly-shaped elements (e.g., hyperboloids or hyperbolic paraboloids). The ability to recognize such elements within the shapes of FACT, therefore, enables designers to consider a larger body of solution options that satisfy a broader range of kinematic, elastomechanical, and dynamic design requirements. Example flexure systems that consist of flexure elements, generated using this theory, are provided as case studies.

Finite Element Model Reduction and Model Updating of structures for Control

Estimation and control of unmeasurable performance variables in complex large-scale systems is an important issue in systems and control. The preferred solution to this problem is to have a relatively low-order and accurate standard plant model which can be used for control purposes. For this purpose, a two-step procedure is proposed. The first step is to generate a reduced Finite Element (FE) model based on the selection of desired Degrees Of Freedom (DOFs), resulting in reduced-order mass, damping, and stiffness matrices. The second step is updating of the reduced-order FE model that is carried out to minimize the differences between the model and the measurements from the structure with the focus on input-output behavior. The presented approach helps to create sufficiently accurate reduced-order dynamic models which can be used for control purposes. The approach will be examined on a planar plate FE model.

Designing hybrid flexure systems and elements using Freedom and Constraint Topologies

Abstract. In this paper we introduce the principles necessary to synthesize hybrid flexure systems and elements. Flexure systems consist of rigid bodies that are joined together by flexure elements that elastically deform to guide the system's rigid bodies with desired degrees of freedom (DOFs). The principles introduced here for synthesizing hybrid flexure systems and elements are extensions of the Freedom and Constraint Topologies (FACT) synthesis approach. FACT utilizes a comprehensive library of geometric shapes from which designers can rapidly consider and compare a multiplicity of flexure concepts that achieve any desired set of DOFs. Prior to this paper, designers primarily used these shapes to synthesize parallel and serial flexure systems and elements. With this paper, designers may now use these same shapes to synthesize more general flexures that consist of various combinations of parallel and serial systems and elements (i.e., hybrid configurations). As such, designers can access a larger body of flexure solutions that satisfy demanding design requirements. Instructions for helping designers utilize or avoid the advantages and challenges of over-, under-, and exact-constraint are also provided. Hybrid systems and elements are analysed and designed as case studies.

Synthesizing Parallel Flexures That Mimic the Kinematics of Serial Flexures Using Freedom and Constraint Topologies

The principles of the freedom and constraint topologies (FACT) synthesis approach are adapted and applied to the design of parallel flexure systems that mimic degrees of freedom (DOFs) primarily achievable by serial flexure systems. FACT provides designers with a comprehensive library of geometric shapes. These shapes enable designers to visualize the regions wherein compliant flexure elements may be placed for achieving desired DOFs. By displacing these shapes far from the point of interest of the stage of a flexure system, designers can compare a multiplicity of concepts that utilizes the advantages of both parallel and serial systems. A complete list of which FACT shapes mimic which DOFs when displaced far from the point of interest of the flexure system's stage is provided as well as an intuitive approach for verifying the completeness of this list. The proposed work intends to cater to the design of precision motion stages, optical mounts, microscopy stages, and general purpose flexure bearings. Two case studies are provided to demonstrate the application of the developed procedure.