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### Guest Editorial

J. Mechanisms Robotics. 2017;9(2):020301-020301-1. doi:10.1115/1.4036028.

The Mechanisms and Robotics Conference has traditionally provided a vigorous and stimulating international forum for the exchange of technical and scientific information on the theory and practice of mechanical systems. The topical coverage has spanned areas central to mechanical systems including design (novel mechanisms and robots and synthesis), analysis (kinematics, dynamics, computational approaches, and software systems), applications including micro air vehicles, modular robotics, origami applications, medical robotics, and exoskeleton-assistive systems, and educational practices.

Commentary by Dr. Valentin Fuster

### Research Papers

J. Mechanisms Robotics. 2017;9(2):021001-021001-6. doi:10.1115/1.4035801.

This paper presents a one-degree-of-freedom network of Bennett linkages which can be deployed to approximate a cylindrical surface. The geometry of the unit mechanism is parameterized and its position kinematics is solved. The influence of the geometric parameters on the deployed shape is examined. Further kinematic analysis isolates those Bennett geometries for which a cylindrical network can be constructed. The procedure for connecting the unit mechanisms in a deployable cylinder is described in detail and used to gain insight into, and formulate some general guidelines for, the design of linkage networks which unfold as curved surfaces. Case studies of deployable structures in the shape of circular and elliptical cylinders are presented. Modeling and simulation validate the proposed approach.

Commentary by Dr. Valentin Fuster
J. Mechanisms Robotics. 2017;9(2):021002-021002-7. doi:10.1115/1.4035559.

Rigidly foldable origami tubes with open ends have been reported in the past. Here, using a mechanism construction process, we show that these tubes can be used as building blocks to form new tubes that are rigidly foldable with a single degree-of-freedom (SDOF). A combination process is introduced, together with a possibility of inserting new facets into an existing tube. The approach can be applied to both single and multilayered tubes with a straight or curved profile. Our work provides designers great flexibility in the design of tubular structures that require large shape change. The results can be readily utilized to build new structures for engineering applications ranging from deployable structures, meta-materials to origami robots.

Commentary by Dr. Valentin Fuster
J. Mechanisms Robotics. 2017;9(2):021003-021003-8. doi:10.1115/1.4035683.

This paper presents the static analysis of elastic force and torque limiters that aim at limiting the forces that a robotic manipulator can apply on its environment. First, the design of one-degree-of-freedom force and torque limiting mechanisms is presented. It is shown that a single elastic component (spring) can be used to provide a prescribed preload and stiffness in both directions of motion along a given axis. Then, the mechanisms are analyzed in order to determine the nonlinear relationships between the motion of the mechanism and the extension of the spring. These relationships can then be used in the design of the force and torque limiters. Finally, the force capabilities of the mechanisms are investigated and numerical results are provided for example designs.

Topics: Torque , Design , Springs
Commentary by Dr. Valentin Fuster
J. Mechanisms Robotics. 2017;9(2):021004-021004-8. doi:10.1115/1.4035544.

Usage of compliant micromechanical oscillators has increased in recent years, due to their reliable performance despite the growing demand for miniaturization. However, ambient vibrations affect the momentum of such oscillators, causing inaccuracy, malfunction, or even failure. Therefore, this paper presents a compliant force-balanced mechanism based on rectilinear motion, enabling usage of prismatic oscillators in translational accelerating environments. The proposed mechanism is based on the opposite motion of two coplanar prismatic joints along noncollinear axes via a shape-optimized linkage system. Rigid-body replacement with shape optimized X-bob, Q-LITF, and LITF joints yielded a harmonic (R > 0.999), low frequency ($f=27 Hz$) single piece force-balanced micromechanical oscillator ($∅$ 35 mm). The experimental evaluation of large-scale prototypes showed a low ratio of the center of mass (CoM) shift compared to the stroke of the device ($≈$ 0.01) and proper decoupling of the mechanism from the base, as the oscillating frequency of the balanced devices during ambient disturbances was unaffected, whereas unbalanced devices had frequency deviations up to 1.6%. Moreover, the balanced device reduced the resultant inertial forces transmitted to the base by 95%.

Commentary by Dr. Valentin Fuster
J. Mechanisms Robotics. 2017;9(2):021005-021005-8. doi:10.1115/1.4035967.

In this work, a new method is introduced for solving large polynomial systems for the kinematic synthesis of linkages. The method is designed for solving systems with degrees beyond 100,000, which often are found to possess quantities of finite roots that are orders of magnitude smaller. Current root-finding methods for large polynomial systems discover both finite and infinite roots, although only finite roots have meaning for engineering purposes. Our method demonstrates how all infinite roots can be precluded in order to obtain substantial computational savings. Infinite roots are avoided by generating random linkage dimensions to construct startpoints and start systems for homotopy continuation paths. The method is benchmarked with a four-bar path synthesis problem.

Commentary by Dr. Valentin Fuster
J. Mechanisms Robotics. 2017;9(2):021006-021006-8. doi:10.1115/1.4035561.

This paper presents a single-degree-of-freedom (single-DoF) gravity balancer that can deal with variable payload without requesting manual or other auxiliary adjustment. The proposed design is an integration of two mechanism modules, i.e., a standard spring-based statically balanced mechanism and a spring adjusting mechanism. A tensile spring is attached to the statically balanced mechanism for balancing the payload, and its installation points are controlled by two cables, which are driven by the spring adjusting mechanism. When different payloads are applied, the spring adjusting mechanism will act to regulate the spring installation points to suitable places such that the overall potential energy of the mechanism and the (variable) payload remains constant within the workspace of the balancer. This therefore suggests the main novelty of the proposed design where the balancer mechanism can automatically sense and respond the change of the payload without manual adjustment to the balancing mechanism. A prototype is built up and successfully tested for the proposed concept.

Commentary by Dr. Valentin Fuster
J. Mechanisms Robotics. 2017;9(2):021007-021007-9. doi:10.1115/1.4035799.

In this paper, a new design is presented for shape morphing using parameterized curves. Inspired by minimal actuation effort, a multiloop linkage is designed with a single input, allowing a morphing curve to take on three distinct shapes. The underlying design is based on a network of four-bar linkages connected together to form a multiloop linkage, referred to as the curve adaptive linkage array (CALA). A three-step method is developed and presented here to find the geometric dimensions of the CALA. The proposed solution is based on the simultaneous recursive solving of the traditional single-loop dyad equations for multiple loops. The key in obtaining a feasible solution is through parameterization of the curves that the linkage is required to morph. To show the effectiveness of the method, an airfoil morphing application is presented, solved using the proposed method, and validated by a prototype. The presented synthesis method provides an effective means for designing a multiloop linkage with a single input.

Commentary by Dr. Valentin Fuster
J. Mechanisms Robotics. 2017;9(2):021008-021008-9. doi:10.1115/1.4035558.

When actuating a rigid origami mechanism by applying moments at the crease lines, we often confront the bifurcation problem where it is not possible to predict the way the model will fold when it is in a flat state. In this paper, we develop a mathematical model of self-folding and propose the concept of self-foldability of rigid origami when a set of moments, which we call a driving force, are applied. In particular, we desire to design a driving force such that a given crease pattern can uniquely self-fold to a desired mode without getting caught in a bifurcation. We provide necessary conditions for self-foldability that serve as tools to analyze and design self-foldable crease patterns. Using these tools, we analyze the unique self-foldability of several fundamental patterns and demonstrate the usefulness of the proposed model for mechanical design.

Commentary by Dr. Valentin Fuster
J. Mechanisms Robotics. 2017;9(2):021009-021009-9. doi:10.1115/1.4035878.

This paper presents a general method to perform simultaneous topological and dimensional synthesis for planar rigid-body morphing mechanisms. The synthesis is framed as a multi-objective optimization problem for which the first objective is to minimize the error in matching the desired shapes. The second objective is typically to minimize the actuating force/moment required to move the mechanism, but different applications may require a different choice. All the possible topologies are enumerated for morphing mechanism designs with a specified number of degrees of freedom (DOF), and infeasible topologies are removed from the search space. A multi-objective genetic algorithm (GA) is then used to simultaneously handle the discrete nature of the topological optimization and the continuous nature of the dimensional optimization. In this way, candidate solutions from any of the feasible topologies enumerated can be evaluated and compared. Ultimately, the method yields a sizable population of viable solutions, often of different topologies, so that the designer can manage engineering tradeoffs in selecting the best mechanism. Three examples illustrate the strengths of this method. The first examines the advantages gained by considering and optimizing across all the topologies simultaneously. The second and third demonstrate the method's versatility by incorporating prismatic joints into the morphing chain to allow for morphing between shapes that have significant changes in both shape and arc length.

Topics: Chain , Design , Topology , Errors
Commentary by Dr. Valentin Fuster
J. Mechanisms Robotics. 2017;9(2):021010-021010-11. doi:10.1115/1.4035684.

This paper proposes an approach for using force-controlled exploration data to update and register an a priori virtual fixture geometry to a corresponding deformed and displaced physical environment. An approach for safe exploration implementing hybrid motion/force control is presented on the slave robot side. During exploration, the shape and the local surface normals of the environment are estimated and saved in an exploration data set. The geometric data collected during this exploration scan are used to deform and register the a priori environment model to the exploration data set. The environment registration is achieved using a deformable registration based on the coherent point drift method. The task-description of the high-level assistive telemanipulation law, called a virtual fixture (VF), is then deformed and registered in the new environment. The new model is updated and used within a model-mediated telemanipulation framework. The approach is experimentally validated using a da-Vinci research kit (dVRK) master interface, a dVRK patient side manipulator, and a Cartesian stage robot. Experiments demonstrate that the updated VF and the updated model allow the users to improve their path following performance and to shorten their completion time when the updated path following VF is applied. The approach presented has direct bearing on a multitude of surgical applications including force-controlled ablation.

Commentary by Dr. Valentin Fuster
J. Mechanisms Robotics. 2017;9(2):021011-021011-11. doi:10.1115/1.4035994.

Flapping-wing flight is a challenging system integration problem for designers due to tight coupling between propulsion and flexible wing subsystems with variable kinematics. High fidelity models that capture all the subsystem interactions are computationally expensive and too complex for design space exploration and optimization studies. A combination of simplified modeling and validation with experimental data offers a more tractable approach to system design and integration, which maintains acceptable accuracy. However, experimental data on flapping-wing aerial vehicles which are collected in a static laboratory test or a wind tunnel test are limited because of the rigid mounting of the vehicle, which alters the natural body response to flapping forces generated. In this study, a flapping-wing aerial vehicle is instrumented to provide in-flight data collection that is unhindered by rigid mounting strategies. The sensor suite includes measurements of attitude, heading, altitude, airspeed, position, wing angle, and voltage and current supplied to the drive motors. This in-flight data are used to setup a modified strip theory aerodynamic model with physically realistic flight conditions. A coupled model that predicts wing motions is then constructed by combining the aerodynamic model with a model of flexible wing twist dynamics and enforcing motor torque and speed bandwidth constraints. Finally, the results of experimental testing are compared to the coupled modeling framework to establish the effectiveness of the proposed approach for improving predictive accuracy by reducing errors in wing motion specification.

Topics: Wings , Flight , Strips , Modeling
Commentary by Dr. Valentin Fuster
J. Mechanisms Robotics. 2017;9(2):021012-021012-13. doi:10.1115/1.4035966.

A concept recently proposed by the authors is that of a multifield sheet that folds into several distinct shapes based on the applied field, be it magnetic, electric, or thermal. In this paper, the design, fabrication, and modeling of a multifield bifold are presented, which utilize magneto-active elastomer (MAE) to fold along one axis and an electro-active polymer, P(VDF-TrFE-CTFE) terpolymer, to fold along the other axis. In prior work, a dynamic model of self-folding origami was developed, which approximated origami creases as revolute joints with torsional spring–dampers and simulated the effect of magneto-active materials on origami-inspired designs. In this work, the crease stiffness and MAE models are discussed in further detail, and the dynamic model is extended to include the effect of electro-active polymers (EAP). The accuracy of this approximation is validated using experimental data from a terpolymer-actuated origami design. After adjusting crease stiffness within the dynamic model, it shows good correlation with experimental data, indicating that the developed EAP approximation is accurate. With the capabilities of the dynamic model improved by the EAP approximation method, the multifield bifold can be fully modeled. The developed model is compared to the experimental data obtained from a fabricated multifield bifold and is found to accurately predict the experimental fold angles. This validation of the crease stiffness, MAE, and EAP models allows for more complicated multifield applications to be designed with confidence in their simulated performance.

Commentary by Dr. Valentin Fuster
J. Mechanisms Robotics. 2017;9(2):021013-021013-17. doi:10.1115/1.4035686.

We present a general technique for achieving kinematic single degree of freedom (1DOF) origami-based mechanisms with thick rigid panels using synchronized offset rolling contact elements (SORCEs). We present general design analysis for planar and 3D relative motions between panels and show physically realized examples. The technique overcomes many of the limitations of previous approaches for thick rigidly foldable mechanisms.

Commentary by Dr. Valentin Fuster

### Technical Brief

J. Mechanisms Robotics. 2017;9(2):024501-024501-6. doi:10.1115/1.4035685.

This paper presents the design and analysis of a reduced degree-of-freedom (DOF) robotic modular leg (RML) mechanism. The RML is composed of a two serially connected four-bar mechanisms that utilize mechanical constraints between articulations to maintain a parallel orientation between the foot and body without the use of an actuated ankle. Kinematic and dynamic models are developed for the leg mechanism and used to analyze actuation requirements and aid motor selection. Experimental results of an integrated prototype tracking a desired foot trajectory are analyzed to improve the accuracy and repeatability of the mechanism. The prototype weighs 4.7 kg and measures 368 mm in a fully extended configuration and exhibits a maximum deviation from the straight line support phase equivalent to 5.2 mm.

Commentary by Dr. Valentin Fuster
J. Mechanisms Robotics. 2017;9(2):024502-024502-7. doi:10.1115/1.4036023.

Oscillatory behavior is important for tasks, such as walking and running. We are developing methods for wearable robotics to add energy to enhance or vary the oscillatory behavior based on the system's phase angle. We define a nonlinear oscillator using a forcing function based on the sine and cosine of the system's phase angle that can modulate the amplitude and frequency of oscillation. This method is based on the state of the system and does not use off-line trajectory planning. The behavior of a limit cycle is shown using the Poincaré–Bendixson criterion. Linear and rotational models are simulated using our phase controller. The method is implemented and tested to control a pendulum.

Commentary by Dr. Valentin Fuster
J. Mechanisms Robotics. 2017;9(2):024503-024503-8. doi:10.1115/1.4035882.

This paper describes a mechanism design methodology that draws plane curves which have finite Fourier series parameterizations, known as trigonometric curves. We present three ways to use the coefficients of this parameterization to construct a mechanical system that draws the curve. One uses Scotch yoke mechanisms for each of the terms in the coordinate trigonometric functions, which are then added using a belt or cable drive. The second approach uses two-coupled serial chains obtained from the coordinate trigonometric functions. The third approach combines the coordinate trigonometric functions to define a single-coupled serial chain that draws the plane curve. This work is a version of Kempe's universality theorem that demonstrates that every plane trigonometric curve has a linkage which draws the curve. Several examples illustrate the method including the use of boundary points and the discrete Fourier transform to define the trigonometric curve.

Topics: Chain
Commentary by Dr. Valentin Fuster
J. Mechanisms Robotics. 2017;9(2):024504-024504-10. doi:10.1115/1.4035899.

In this paper, we have presented a unified framework for generating planar four-bar motions for a combination of poses and practical geometric constraints and its implementation in MotionGen app for Apple's iOS and Google's Android platforms. The framework is based on a unified type- and dimensional-synthesis algorithm for planar four-bar linkages for the motion-generation problem. Simplicity, high-utility, and wide-spread adoption of planar four-bar linkages have made them one of the most studied topics in kinematics leading to development of algorithms and theories that deal with path, function, and motion generation problems. Yet to date, there have been no attempts to develop efficient computational algorithms amenable to real-time computation of both type and dimensions of planar four-bar mechanisms for a given motion. MotionGen solves this problem in an intuitive fashion while providing high-level, rich options to enforce practical constraints. It is done effectively by extracting the geometric constraints of a given motion to provide the best dyad types as well as dimensions of a total of up to six four-bar linkages. The unified framework also admits a plurality of practical geometric constraints, such as imposition of fixed and moving pivot and line locations along with mixed exact and approximate synthesis scenarios.

Commentary by Dr. Valentin Fuster

J. Mechanisms Robotics. 2017;9(2):025001-025001-9. doi:10.1115/1.4036014.

This paper presents the design, analysis, and testing of a fully actuated modular spherical tensegrity robot for co-robotic and space exploration applications. Robots built from tensegrity structures (composed of pure tensile and compression elements) have many potential benefits including high robustness through redundancy, many degrees-of-freedom in movement and flexible design. However, to take full advantage of these properties, a significant fraction of the tensile elements should be active, leading to a potential increase in complexity, messy cable, and power routing systems and increased design difficulty. Here, we describe an elegant solution to a fully actuated tensegrity robot: The TT-3 (version 3) tensegrity robot, developed at UC Berkeley, in collaboration with NASA Ames, is a lightweight, low cost, modular, and rapidly prototyped spherical tensegrity robot. This robot is based on a ball-shaped six-bar tensegrity structure and features a unique modular rod-centered distributed actuation and control architecture. This paper presents the novel mechanism design, architecture, and simulations of TT-3, an untethered, fully actuated cable-driven six-bar spherical tensegrity robot. Furthermore, this paper discusses the controls and preliminary testing performed to observe the system's behavior and performance and is evaluated against previous models of tensegrity robots developed at UC Berkeley and elsewhere.

Commentary by Dr. Valentin Fuster
J. Mechanisms Robotics. 2017;9(2):025002-025002-11. doi:10.1115/1.4035863.

A wide range of engineering applications, ranging from civil to space structures, could benefit from the ability to construct material-efficient lattices that are easily reconfigurable. The challenge preventing modular robots from being applied at large scales is mainly the high level of complexity involved in duplicating a large number of highly integrated module units. We believe that reconfigurability can be more effectively achieved at larger scales by separating the structural design from the rest of the functional components. To this end, we propose a modular chainlike structure of links and connector nodes that can be used to fold a wide range of two-dimensional (2D) or three-dimensional (3D) structural lattices that can be easily disassembled and reconfigured when desired. The node geometry consists of a diamondlike shape that is one-twelfth of a rhombic dodecahedron, with magnets embedded on the faces to allow a forceful and self-aligning connection with neighboring links. After describing the concept and design, we demonstrate a prototype consisting of 350 links and experimentally show that objects with different shapes can be successfully approximated by our proposed chain design.

Commentary by Dr. Valentin Fuster