A novel three-dimensional elliptical vibration cutting device based on the freedom and constraint topologies theory

Aiming at the issue of the lack of the design theory for the three-dimensional elliptical vibration cutting device, a compliant mechanism with two rotations and one translation is synthesized based on the theory of freedom and constraint topologies. And a three-dimensional elliptical vibration cutting device is proposed on the basis of the compliant mechanism. The relationship between the critical speed and the length of the tool bar is analyzed. Simulation is conducted to analyze the influence of parameters on the output ellipse. Experiments are conducted to verify the validity of the elliptical vibration cutting device. The relationship between the roughness and the cutting speed is obtained. Experiments with different driving frequencies are conducted without the change of other parameters. Results show that the proposed compliant mechanism is feasible for the elliptical vibration cutting device. Compared with the common cutting, the new elliptical vibration cutting device has a better performance in the processing effect. This provides an important reference for design of the elliptical vibration cutting device.

Optimizing the Geometry of Flexure System Topologies Using the Boundary Learning Optimization Tool

We introduce a new computational tool called the Boundary Learning Optimization Tool (BLOT) that identifies the boundaries of the performance capabilities achieved by general flexure system topologies if their geometric parameters are allowed to vary from their smallest allowable feature sizes to their largest geometrically compatible feature sizes for given constituent materials. The boundaries generated by the BLOT fully define the design spaces of flexure systems and allow designers to visually identify which geometric versions of their synthesized topologies best achieve desired combinations of performance capabilities. The BLOT was created as a complementary tool to the freedom and constraint topologies (FACT) synthesis approach in that the BLOT is intended to optimize the geometry of the flexure topologies synthesized using the FACT approach. The BLOT trains artificial neural networks to create models of parameterized flexure topologies using numerically generated performance solutions from different design instantiations of those topologies. These models are then used by an optimization algorithm to plot the desired topology’s performance boundary. The model-training and boundary-plotting processes iterate using additional numerically generated solutions from each updated boundary generated until the final boundary is guaranteed to be accurate within any average error set by the user. A FACT-synthesized flexure topology is optimized using the BLOT as a simple case study.

Geometry Optimization of Flexure System Topologies Using the Boundary Learning Optimization Tool (BLOT)

In this paper, we introduce a new computational tool called the Boundary Learning Optimization Tool (BLOT) that rapidly identifies the boundary of the performance capabilities achieved by a general flexure topology if its geometric parameters are allowed to vary from their smallest allowable feature sizes to the largest geometrically compatible feature sizes for a given constituent material. The boundaries generated by the BLOT fully define a flexure topology’s design space and allow designers to visually identify which geometric versions of their synthesized topology best achieve a desired combination of performance capabilities. The BLOT was created as a complementary tool to the Freedom And Constraint Topologies (FACT) synthesis approach in that the BLOT is intended to optimize the geometry of the flexure topologies synthesized using the FACT approach. The BLOT trains artificial neural networks to create sufficiently accurate models of parameterized flexure topologies using the fewest number of design instantiations and their corresponding numerically generated performance solutions. These models are then used by an efficient algorithm to plot the desired topology’s performance boundary. A FACT-synthesized flexure topology is optimized using the BLOT as a case study.

A Visualization Approach for Analyzing and Synthesizing Serial Flexure Elements

In this paper, we extend the principles of the freedom and constraint topologies (FACT) synthesis approach such that designers can analyze and synthesize serial flexure elements—not to be confused with serial flexure systems. Unlike serial systems, serial elements do not possess intermediate rigid bodies within their geometry and thus avoid the negative effects of unnecessary mass and underconstrained bodies that generate uncontrolled vibrations. Furthermore, in comparison with other common parallel flexure elements such as wire, blade, and living hinge flexures, serial elements can be used within flexure systems to achieve (i) a larger variety of kinematics, (ii) more dynamic and elastomechanic versatility, and (iii) greater ranges of motion. Here, we utilize the principles of FACT to intuitively guide designers in visualizing a multiplicity of serial flexure element geometries that can achieve any desired set of degrees of freedom (DOFs). Using this approach, designers can rapidly generate a host of new serial flexure elements for synthesizing advanced flexure systems. Thirty seven serial flexure elements are provided as examples, and three flexure systems that consist of some of these elements are synthesized as 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.

Synthesizing 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 Tri-Chamber 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 validate their FACT-predicted kinematics. Examples are provided as case studies.

Designing hybrid flexure systems and elements using Freedom and Constraint Topologies

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.

Analyzing and Designing Serial Flexure Elements

In this paper we introduce the principles necessary to analyze and design serial flexure elements, which may be used to synthesize advanced compliant mechanisms (CMs). The most commonly used flexure elements (e.g., wire, blade, or living hinge flexures) are often parallel and thus impose constraining forces directly through all parts of their geometry to the rigid bodies that they join within the CM. Serial flexure elements, on the other hand, constrain rigid bodies with a larger variety of forces and moments and thus enable CMs to achieve (i) more degrees of freedom (DOFs), (ii) larger dynamic and elastomechanic versatility, and (iii) greater ranges of motion than parallel elements. In this paper, we extend the principles of the Freedom and Constraint Topologies (FACT) synthesis approach such that it enables the synthesis of CMs that are not only constrained by parallel flexure elements, but also by serial elements. FACT utilizes geometric shapes to intuitively guide designers in visualizing compliant element geometries that achieve any desired set of DOFs. In this way, designers can rapidly generate a host of new serial flexure elements for various CM applications. Such elements are provided here 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.

Designing Microstructural Architectures With Thermally Actuated Properties Using Freedom, Actuation, and Constraint Topologies

In this paper, we demonstrate how the principles of the freedom, actuation, and constraint topologies (FACT) approach may be applied to the synthesis, analysis, and optimization of microstructural architectures that possess extreme or unusual thermal expansion properties (e.g., zero or large negative-thermal expansion coefficients). FACT provides designers with a comprehensive library of geometric shapes, which may be used to visualize the regions wherein various microstructural elements can be placed for achieving desired bulk material properties. In this way, designers can rapidly consider and compare a multiplicity of microstructural concepts that satisfy the desired design requirements before selecting the final concept. A complementary analytical tool is also provided to help designers rapidly calculate and optimize the desired thermal properties of the microstructural concepts that are generated using FACT. As a case study, this tool is used to calculate the negative-thermal expansion coefficient of a microstructural architecture synthesized using FACT. The result of this calculation is verified using a finite element analysis (FEA) package called ale3d.