Hai-Jun Su

Programmable motion of DNA origami mechanisms

Significance Folding DNA into complex 3D shapes (DNA origami) has emerged as a powerful method for the precise design and fabrication of self-assembled nanodevices. Current efforts have focused largely on developing static objects or structures with small movements and/or unspecified motion paths. Here we establish a basis for developing DNA-based nanomachines by creating dynamic mechanisms with well-defined motion. We demonstrate the design of nanoscale 1D, 2D, and 3D motion by integrating concepts from engineering machine design with DNA origami nanotechnology. DNA origami enables the precise fabrication of nanoscale geometries. We demonstrate an approach to engineer complex and reversible motion of nanoscale DNA origami machine elements. We first design, fabricate, and characterize the mechanical behavior of flexible DNA origami rotational and linear joints that integrate stiff double-stranded DNA components and flexible single-stranded DNA components to constrain motion along a single degree of freedom and demonstrate the ability to tune the flexibility and range of motion. Multiple joints with simple 1D motion were then integrated into higher order mechanisms. One mechanism is a crank–slider that couples rotational and linear motion, and the other is a Bennett linkage that moves between a compacted bundle and an expanded frame configuration with a constrained 3D motion path. Finally, we demonstrate distributed actuation of the linkage using DNA input strands to achieve reversible conformational changes of the entire structure on ∼minute timescales. Our results demonstrate programmable motion of 2D and 3D DNA origami mechanisms constructed following a macroscopic machine design approach.

A Pseudorigid-Body 3R Model for Determining Large Deflection of Cantilever Beams Subject to Tip Loads

In this paper, a pseudo-rigid-body (PRB) 3R model which consists of four rigid links joined by three revolute joints and three torsion springs is proposed for approximating the de∞ection of a cantilever beam subject to a general tip load. The large de∞ection beam equations are solved through numerical integration. A comprehensive atlas of the tip de∞ection for various load modes is obtained. A three-dimensional search routine has been developed to flnd the optimal set of characteristic radius factors and spring stifiness of the PRB 3R model. Detailed error analysis has been done by comparing with the pre-computed tip de∞ection atlas. Our results show that the approximation error is much less than that of the conventional PBR 1R model. The beneflts of the PRB 3R model include (a) load independence which is critical for analysis/synthesis applications where loads vary signiflcantly, (b) high accuracy for large de∞ection beams, and (c) explicit kinematic and static constraint equations which are simpler to solve compared with the flnite element model. To demonstrate the use of the PRB 3R model, a compliant 4-bar linkage is studied and verifled by a numerical example. The result shows a maximum tip de∞ection error of 1:2% compared with the FEA model.

A Screw Theory Approach for the Conceptual Design of Flexible Joints for Compliant Mechanisms

This paper presents a screw theory based approach for the analysis and synthesis of flexible joints using wire and sheet flexures. The focus is on designing flexure systems that have a simple geometry, i.e., a parallel constraint pattern. We provide a systematic formulation of the constraint-based approach, which has been mainly developed by precision engineering experts in designing precision machines. The two fundamental concepts in the constraint-based approach, constraint and freedom, can be represented mathematically by a wrench and a twist in screw theory. For example, an ideal wire flexure applies a translational constraint, which can be described by a wrench of pure force. As a result, the design rules of the constraint-based approach can be systematically formulated in the format of screws and screw systems. Two major problems in compliant mechanism design, constraint pattern analysis, and constraint pattern design are discussed with examples in details. Lastly, a case study is provided to demonstrate the application of this approach to the design of compliant prismatic joints. This innovative method paves the way for introducing computational techniques into the constraint-based approach for the synthesis and analysis of compliant mechanisms.

SHARP: A System for Haptic Assembly and Realistic Prototyping

Virtual Reality (VR) technology holds promise as a virtual prototyping tool for mechanical assembly; however, several developmental challenges still need to be addressed before virtual prototyping applications can successfully be integrated into the product realization process. This paper describes the development of SHARP (System for Haptic Assembly & Realistic Prototyping), a portable VR interface for virtual assembly. SHARP uses physically-based modeling for simulating realistic part-to-part and hand-to-part interactions in virtual environments. A dual handed haptic interface for realistic part interaction using the PHANToM® haptic devices is presented. The capability of creating subassemblies enhances the application’s ability to handle a wide variety of assembly scenarios. Swept volumes are implemented for addressing maintainability issues and a network module is added for communicating with different VR systems at dispersed geographic locations. Support for various types of VR systems allows an easy integration of SHARP into the product realization process resulting in faster product development, faster identification of assembly and design issues and a more efficient and less costly product design process.

Screw Theory Based Methodology for the Deterministic Type Synthesis of Flexure Mechanisms

Flexure mechanism synthesis, however, is still a comparably difficult task. This paper aims at exploring a simple but systematic type synthesis methodology for general flexure mechanisms. The applied mathematical tool is reciprocal screw system theory in geometric form, and the proposed approach is an improvement of freedom and constraint topology (FACT), which is based on the FACT approach, combining with other methods including equivalent compliance mapping, set operation on building blocks, etc. As a result, it enables the type synthesis of flexure mechanisms simple, complete, and effective. What is more significant is that the proposed approach makes the unified type synthesis of both constraint-based and kinematics-based flexure mechanisms available. That is also the new contribution to the flexure de-sign.

DNA Origami Compliant Nanostructures with Tunable Mechanical Properties

DNA origami enables fabrication of precise nanostructures by programming the self-assembly of DNA. While this approach has been used to make a variety of complex 2D and 3D objects, the mechanical functionality of these structures is limited due to their rigid nature. We explore the fabrication of deformable, or compliant, objects to establish a framework for mechanically functional nanostructures. This compliant design approach is used in macroscopic engineering to make devices including sensors, actuators, and robots. We build compliant nanostructures by utilizing the entropic elasticity of single-stranded DNA (ssDNA) to locally bend bundles of double-stranded DNA into bent geometries whose curvature and mechanical properties can be tuned by controlling the length of ssDNA strands. We demonstrate an ability to achieve a wide range of geometries by adjusting a few strands in the nanostructure design. We further developed a mechanical model to predict both geometry and mechanical properties of our compliant nanostructures that agrees well with experiments. Our results provide a basis for the design of mechanically functional DNA origami devices and materials.

A Polynomial Homotopy Formulation of the Inverse Static Analysis of Planar Compliant Mechanisms

This paper formulates the inverse static analysis of planar compliant mechanisms in polynomial form. The goal is to find the equilibrium configurations of the system in response to a known force/moment applied to the mechanism. The geometric constraint of the linkage defines a set of kinematics equations which are combined with equilibrium equations obtained from partial derivatives of the potential-energy function. In order to apply polynomial homotopy solver to these equations, we approximate the linear torsion spring torque at each joint by using sine and cosine functions. The results obtained from the homotopy solver are then refined using Newton-Raphson iteration. To demonstrate the analysis steps, we study two example planar compliant mechanisms, a four-bar linkage with two torsional springs, and a parallel platform supported by three linear springs. Numerical examples are provided together with plots of the potential energy during a movement between selected equilibrium positions.

Algorithm 857: POLSYS_GLP—a parallel general linear product homotopy code for solving polynomial systems of equations

Globally convergent, probability-one homotopy methods have proven to be very effective for finding all the isolated solutions to polynomial systems of equations. After many years of development, homotopy path trackers based on probability-one homotopy methods are reliable and fast. Now, theoretical advances reducing the number of homotopy paths that must be tracked and handling singular solutions have made probability-one homotopy methods even more practical. POLSYS_GLP consists of Fortran 95 modules for finding all isolated solutions of a complex coefficient polynomial system of equations. The package is intended to be used on a distributed memory multiprocessor in conjunction with HOMPACK90 (Algorithm 777), and makes extensive use of Fortran 95-derived data types and MPI to support a general linear product (GLP) polynomial system structure. GLP structure is intermediate between the partitioned linear product structure used by POLSYS_PLP (Algorithm 801) and the BKK-based structure used by PHCPACK. The code requires a GLP structure as input, and although finding the optimal GLP structure is a difficult combinatorial problem, generally physical or engineering intuition about a problem yields a very good GLP structure. POLSYS_GLP employs a sophisticated power series end game for handling singular solutions, and provides support for problem definition both at a high level and via hand-crafted code. Different GLP structures and their corresponding Bezout numbers can be systematically explored before committing to root finding.

A Symbolic Formulation for Analytical Compliance Analysis and Synthesis of Flexure Mechanisms

This paper presents a symbolic formulation for analytical compliance analysis and synthesis of flexure mechanisms with serial, parallel, or hybrid topologies. Our approach is based on the screw theory that characterizes flexure deformations with motion twists and loadings with force wrenches. In this work, we first derive a symbolic formulation of the compliance and stiffness matrices for commonly used flexure elements, flexure joints, and simple chains. Elements of these matrices are all explicit functions of flexure parameters. To analyze a general flexure mechanism, we subdivide it into multiple structural modules, which we identify as serial, parallel, or hybrid chains. We then analyze each module with the known flexure structures in the library. At last, we use a bottom-up approach to obtain the compliance/stiffness matrix for the overall mechanism. This is done by taking appropriate coordinate transformation of twists and wrenches in space. Four practical examples are provided to demonstrate the approach. A numerical example is employed to compare analytical compliance models against a finite element model. The results show that the errors are sufficiently small (2%, compared with finite element (FE) model), if the range of motion is limited to linear deformations. This work provides a systematical approach for compliance analysis and synthesis of general flexure mechanisms. The symbolic formulation enables subsequent design tasks, such as compliance synthesis or sensitivity analysis.

A Desktop Networked Haptic VR Interface for Mechanical Assembly

This paper presents the development of a PC-based 3D human computer interface for virtual assembly applications. This system is capable of importing complex CAD (Computer Aided Design) models, rendering them in stereo, and implementing haptic force feedback for realistic part interaction in virtual environments. Such an application will facilitate wider acceptance of the use of a VR interface for prototyping assembly tasks. This interface provides both visual and haptic feedback to the user, while allowing assembly tasks to be performed on a desktop virtual environment. The network module has the ability to communicate with multiple VR systems (such as CAVE etc.) at geographically dispersed locations using a non-dedicated network channel. The potential benefits of such a system include identification of assembly issues early in the design process where changes can be made easily, resulting in a more efficient and less costly product design process.