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### Editorial

J. Mechanisms Robotics. 2018;10(2):020201-020201-1. doi:10.1115/1.4039203.
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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 span areas central to mechanical systems including design (novel mechanisms and robots, synthesis), analysis (kinematics, dynamics, computational approaches, and software systems), applications (from micro-air vehicles, modular robotics, origami applications, medical robotics, to exoskeleton-assistive systems), and educational practices.

Commentary by Dr. Valentin Fuster

### Research Papers

J. Mechanisms Robotics. 2018;10(2):021001-021001-10. doi:10.1115/1.4038969.
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Modular origami is a type of origami where multiple pieces of paper are folded into modules, and these modules are then interlocked with each other forming an assembly. Some of them turn out to be capable of large-scale shape transformation, making them ideal to create metamaterials with tuned mechanical properties. In this paper, we carry out a fundamental research on two-dimensional (2D) transformable assemblies inspired by modular origami. Using mathematical tiling and patterns and mechanism analysis, we are able to develop various structures consisting of interconnected quadrilateral modules. Due to the existence of 4R linkages within the assemblies, they become transformable, and can be compactly packaged. Moreover, by the introduction of paired modules, we are able to adjust the expansion ratio of the pattern. Moreover, we also show that transformable patterns with higher mobility exist for other polygonal modules. The design flexibility among these structures makes them ideal to be used for creation of truly programmable metamaterials.

Commentary by Dr. Valentin Fuster
J. Mechanisms Robotics. 2018;10(2):021002-021002-8. doi:10.1115/1.4038976.
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This paper proposes a novel method for analyzing linear series elastic actuators (SEAs) in a parallel-actuated Stewart platform, which has full six degrees-of-freedom (DOF) in position and orientation. SEAs can potentially provide a better human–machine interface for the user. However, in the study of parallel-actuated systems with full 6DOF, the effect of compliance in series with actuators has not been adequately studied from the perspective of wrench capabilities. We found that some parameters of the springs and the stroke lengths of the linear actuators play a major role in the actuation limits of the system. This is an important consideration when adding SEAs into a Stewart platform or other parallel-actuated robots to improve their human usage.

Commentary by Dr. Valentin Fuster
J. Mechanisms Robotics. 2018;10(2):021003-021003-8. doi:10.1115/1.4038970.
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This paper presents the design and development of a new type of piezoelectric-driven robot, which consists of a piezoelectric unimorph actuator integrated as part of the structure of a four-bar linkage to generate locomotion. The unimorph actuator replaces the input link of the four-bar linkage, and motion is generated at the coupler link due to the actuator deflection. A dimensional synthesis approach is proposed for the design of four-bar linkage that amplifies the small displacement of the piezoelectric actuator at the coupler link. The robot consists of two such piezo-driven four-bar linkages, and its gait cycle is described. The robot's speed is derived through kinematic modeling and experimentally verified using a fabricated prototype. The robot prototype's performance in terms of its payload capability and nominal operating power is also characterized experimentally. These results will be important for developing a motion planning control strategy for a autonomous robot locomotion, which will be part of future work.

Commentary by Dr. Valentin Fuster
J. Mechanisms Robotics. 2018;10(2):021004-021004-11. doi:10.1115/1.4038972.
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We present a design technique for generating rigidly foldable quadrilateral meshes (RFQMs), taking as input four arrays of direction angles and fold angles for horizontal and vertical folds. By starting with angles, rather than vertex coordinates, and enforcing the fold-angle multiplier condition at each vertex, it is possible to achieve arbitrarily large and complex panel arrays that flex from unfolded to flatly folded with a single degree-of-freedom (DOF). Furthermore, the design technique is computationally simple, reducing for some cases to a simple linear-programming problem. The resulting mechanisms have applications in architectural facades, furniture design, and more.

Commentary by Dr. Valentin Fuster
J. Mechanisms Robotics. 2018;10(2):021005-021005-8. doi:10.1115/1.4038980.
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We consider planar navigation for a polygonal, holonomic robot in an obstacle-filled environment in SE(2). To determine the free space, we first represent obstacles as point clouds in the robot configuration space (C). A point-wise Minkowski sum of the robot and obstacle points is then calculated in C using obstacle points and robot convex hull points for varying robot configurations. Using graph search, we obtain a seed path, which is used in our novel method to compute overlapping convex regions for consecutive seed path chords. The resulting regions provide collision-free space useful for finding feasible trajectories that optimize a specified cost functional. The key contribution is the proposed method's ability to easily generate a set of convex, overlapping polytopes that effectively represent the traversable free space. This, in turn, lends itself to (a) efficient computation of optimal paths in $ℝ3$ and (b) extending these basic ideas to the special Euclidean space SE(2). We provide simulated examples and implement this algorithm on a KUKA youBot omnidirectional base.

Commentary by Dr. Valentin Fuster
J. Mechanisms Robotics. 2018;10(2):021006-021006-10. doi:10.1115/1.4038977.
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This paper presents a new mechanics-based framework for the qualitative analysis and conceptual design of mechanical metamaterials, and specifically materials exhibiting auxetic behavior. The methodology is inspired by recent advances in the insightful synthesis of compliant mechanisms by visualizing a kinetostatic field of forces that flow through the mechanism geometry. The framework relates load flow in the members of the microstructure to the global material properties, thereby enabling a novel synthesis technique for auxetic microstructures. This understanding is used to qualitatively classify auxetic materials into two classes, namely, high-shear and low-shear microstructures. The ability to achieve additional attributes such as isotropy is shown to be related to the qualitative class that the microstructure belongs.

Commentary by Dr. Valentin Fuster
J. Mechanisms Robotics. 2018;10(2):021007-021007-10. doi:10.1115/1.4038971.
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This paper introduces a new architecture of spherical parallel robot which significantly extends the workspace when compared to existing architectures. To this end, the singularity locus is studied and the design parameters are chosen so as to confine the singularities to areas already limited by other constraints such as mechanical interferences. First, the architecture of the spherical redundant robot is presented and the Jacobian matrices are derived. Afterwards, the analysis of the singularities is addressed from a geometric point of view, which yields a description of the singularity locus expressed as a function of the architectural parameters. Then, the results are applied to an example set of architectural parameters, which are chosen in order to illustrate the advantages of the redundant architecture over current designs in terms of workspace.

Commentary by Dr. Valentin Fuster
J. Mechanisms Robotics. 2018;10(2):021008-021008-12. doi:10.1115/1.4039121.
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For more than a century, rigid-body displacements have been viewed as affine transformations described as homogeneous transformation matrices wherein the linear part is a rotation matrix. In group-theoretic terms, this classical description makes rigid-body motions a semidirect product. The distinction between a rigid-body displacement of Euclidean space and a change in pose from one reference frame to another is usually not articulated well in the literature. Here, we show that, remarkably, when changes in pose are viewed from a space-fixed reference frame, the space of pose changes can be endowed with a direct product group structure, which is different from the semidirect product structure of the space of motions. We then show how this new perspective can be applied more naturally to problems such as monitoring the state of aerial vehicles from the ground, or the cameras in a humanoid robot observing pose changes of its hands.

Commentary by Dr. Valentin Fuster
J. Mechanisms Robotics. 2018;10(2):021009-021009-13. doi:10.1115/1.4038978.
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A theoretical–algorithmic framework for the construction of balance stability boundaries of biped robots with multiple contacts with the environment is proposed and implemented on a robotic platform. Comprehensive and univocal definitions of the states of balance of a generic legged system are introduced with respect to the system's contact configuration. Theoretical models of joint-space and center of mass (COM)-space dynamics under multiple contacts, distribution of contact wrenches, and robotic system parameters are established for their integration into a nonlinear programing (NLP) problem. In the proposed approach, the balance stability capabilities of a biped robot are quantified by a partition of the state space of COM position and velocity. The boundary of such a partition provides a threshold between balanced and falling states of the biped robot with respect to a specified contact configuration. For a COM state to be outside of the stability boundary represents the sufficient condition for falling, from which a change in the system's contact is inevitable. Through the calculated stability boundaries, the effects of different contact configurations (single support (SS) and double support (DS) with different step lengths) on the robot's balance stability capabilities can be quantitatively evaluated. In addition, the balance characteristics of the experimental walking trajectories of the robot at various speeds are analyzed in relation to their respective stability boundaries. The proposed framework provides a contact-dependent balance stability criterion for a given system, which can be used to improve the design and control of walking robots.

Commentary by Dr. Valentin Fuster
J. Mechanisms Robotics. 2018;10(2):021010-021010-8. doi:10.1115/1.4039342.
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An experimental prosthetic foot intended for evaluating a novel design objective is presented. This objective, called the lower leg trajectory error (LLTE), enables the optimization of passive prosthetic feet by modeling the trajectory of the shank during single support for a given prosthetic foot and selecting design variables that minimize the error between this trajectory and able-bodied kinematics. A light-weight, fully characterized test foot with variable ankle joint stiffness was designed to evaluate the LLTE. The test foot can replicate the range of motion of a physiological ankle over a range of different ankle joint stiffnesses. The test foot consists of a rotational ankle joint machined from acetal resin, interchangeable U-shaped nylon springs that range from 1.5 N · m/deg to 24 N · m/deg, and a flexible nylon forefoot with a bending stiffness of 16 N · m2. The U-shaped springs were designed to support a constant moment along their length to maximize strain energy density; this feature was critical in creating a high-stiffness and high-range of motion ankle. The design performed as predicted during mechanical and in vivo testing, and its modularity allowed us to rapidly vary the ankle joint stiffness. Qualitative feedback from preliminary testing showed that this design is ready for use in large scale clinical trials to further evaluate the use of the LLTE as an optimization objective for passive prosthetic feet.

Commentary by Dr. Valentin Fuster

### Technical Brief

J. Mechanisms Robotics. 2018;10(2):024501-024501-9. doi:10.1115/1.4039101.
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Fiber-reinforced elastomeric enclosures (FREEs) generate sophisticated motions, when pressurized, including axial rotation, extension, and compression, and serve as fundamental building blocks for soft robots in a variety of applications. However, most modeling techniques employed by researchers do not capture the key characteristics of FREEs to enable development of robust design and control schemes. Accurate and computationally efficient models that capture the nonlinearity of fibers and elastomeric components are needed. This paper presents a continuum model that captures the nonlinearities of the fiber and elastomer components as well as nonlinear relationship between applied pressure, deformation, and output forces and torque. One of the key attributes of this model is that it captures the behavior of FREEs in a computationally tractable manner with a minimum burden on experimental parameter determination. Without losing generality of the model, we validate it for a FREE with one fiber family, which is the simplest system exhibiting a combination of elongation and twist when pressurized. Experimental data in multiple kinematic configurations show agreement between our model prediction and the moments that the actuators generate. The model can be used to not only determine operational parameters but also to solve inverse problems, i.e., in design synthesis.

Commentary by Dr. Valentin Fuster

J. Mechanisms Robotics. 2018;10(2):025001-025001-8. doi:10.1115/1.4038973.
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This paper presents the design of the interacting-BoomCopter (I-BoomCopter) unmanned aerial vehicle (UAV) for mounting a remote sensor package on a vertical surface. Critical to the design is the novel, custom, light-weight passive end effector. The end effector has a forward-facing sonar sensor and in-line force sensor to enable autonomous sensor mounting tasks. The I-BoomCopter's front boom is equipped with a horizontally mounted propeller, which can provide forward and reverse thrust with zero roll and pitch angles. The design and modeling of the updated I-BoomCopter platform is presented along with prototype flight test results. A teleoperated wireless camera sensor mounting task examines the updated platform's suitability for mounting remote sensor packages. Additionally, an autonomous control strategy for remote sensor mounting with the I-BoomCopter is proposed, and autonomous test flights demonstrate the efficacy of the approach.

Commentary by Dr. Valentin Fuster
J. Mechanisms Robotics. 2018;10(2):025002-025002-9. doi:10.1115/1.4038775.
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This paper presents the design and integration of a two-digit robotic exoskeleton glove mechanism. The proposed glove is designed to assist the user with grasping motions, such as the pincer grasp, while maintaining a natural coupling relationship among the finger and thumb joints, resembling that of a normal human hand. The design employs single degree-of-freedom (DOF) linkage mechanisms to achieve active flexion and extension of the index finger and thumb. This greatly reduces the overall weight and size of the system making it ideal for prolonged usage. The paper describes the design, mathematical modeling of the proposed system, detailed electromechanical design, and software architecture of the integrated prototype. The prototype is capable of recording information about the index finger and thumb movements, interaction forces exerted by the finger/thumb on the exoskeleton, and can provide feedback through vibration. In addition, the glove can serve as a standalone device for rehabilitation purposes, such as assisting in achieving tip or pulp pinch. The paper concludes with an experimental validation of the proposed design by comparing the motion produced using the exoskeleton glove on a wooden mannequin with that of a natural human hand.

Commentary by Dr. Valentin Fuster
J. Mechanisms Robotics. 2018;10(2):025003-025003-6. doi:10.1115/1.4038979.
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This paper presents a design procedure to achieve a flapping wing mechanism for a micro-air vehicle that coordinates both the wing swing and wing pitch with one actuator. The mechanism combines a planar four-bar linkage with a spatial four-bar linkage attached to the input and output links forming a six-bar linkage. The planar four-bar linkage was designed to control the wing swing trajectory profile and the spatial four-bar linkage was designed to coordinate the pitch of the wing to the swing movement. Tolerance zones were specified around the accuracy points, which were then sampled to generate a number of design candidates. The result was 29 designs that achieve the desired coordination of wing swing and pitch, and a prototype was constructed.

Topics: Wings , Linkages , Design
Commentary by Dr. Valentin Fuster
J. Mechanisms Robotics. 2018;10(2):025004-025004-8. doi:10.1115/1.4039064.
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The kinematic synthesis of planar linkage mechanisms has traditionally been broken into the categories of motion, path, and function generation. Each of these categories of problems has been solved separately. Many problems in engineering practice require some combination of these problem types. For example, a problem requiring coupler points and/or poses in addition to specific input and/or output link angles that correspond to those positions. A limited amount of published work has addressed some specific underconstrained combinations of these problems. This paper presents a general graphical method for the synthesis of a four bar linkage to satisfy any combination of these exact synthesis problems that is not overconstrained. The approach is to consider the constraints imposed by the target positions on the linkage through the poles and rotation angles. These pole and rotation angle constraints (PRCs) are necessary and sufficient conditions to meet the target positions. After the constraints are made, free choices which may remain can be explored by simply dragging a fixed pivot, a moving pivot, or a pole in the plane. The designer can thus investigate the family of available solutions before making the selection of free choices to satisfy other criteria. The fully constrained combinations for a four bar linkage are given and sample problems are solved for several of them.

Commentary by Dr. Valentin Fuster
J. Mechanisms Robotics. 2018;10(2):025005-025005-8. doi:10.1115/1.4039075.
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We introduce a novel input device for the teleoperation of extensible continuum robots. As opposed to previous works limited by kinematically dissimilar master devices or restricted degrees-of-freedom (DoF), a kinematically similar input device capable of 9DoF is designed and used. The device is capable of achieving configurations identical to a three-section continuum robot and simplifies the teleoperation of such manipulators. In this paper, we outline the design of the input device and its construction. Implementation of the new master device and its effectiveness in regulating a physical system is also discussed.

Commentary by Dr. Valentin Fuster
J. Mechanisms Robotics. 2018;10(2):025006-025006-8. doi:10.1115/1.4038975.
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Here, we present the design, fabrication, and evaluation of a prismatic-revolute-revolute joint hand called the model B that we developed for grasping from ungrounded vehicles. This hand relies on a prismatic proximal joint followed by revolute distal joints in each finger and is actuated by a single motor- and a tendon-based underactuated transmission. We evaluate this design's grasping capabilities both when fully constrained by a robotic arm and when minimally constrained and evaluate its performance in terms of general grasping capabilities and suitability for aerial grasping applications. The evaluation shows that the model B can securely grasp a wide range of objects using a wrap grasp due to the prismatic-revolute-revolute joint finger kinematics. We also show that the prismatic proximal joints and between finger coupling allows the hand to grasp objects under large positional uncertainty without exerting large reaction forces on the object or host vehicle.

Commentary by Dr. Valentin Fuster
J. Mechanisms Robotics. 2018;10(2):025007-025007-7. doi:10.1115/1.4038974.
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This paper introduces an approach for decomposing exploration tasks among multiple unmanned surface vehicles (USVs) in congested regions. In order to ensure effective distribution of the workload, the algorithm has to consider the effects of the environmental constraints on the USVs. The performance of a USV is influenced by the surface currents, risk of collision with the civilian traffic, and varying depths due to tides and weather. The team of USVs needs to explore a certain region of the harbor and we need to develop an algorithm to decompose the region of interest into multiple subregions. The algorithm overlays a two-dimensional grid upon a given map to convert it to an occupancy grid, and then proceeds to partition the region of interest among the multiple USVs assigned to explore the region. During partitioning, the rate at which each USV is able to travel varies with the applicable speed limits at the location. The objective is to minimize the time taken for the last USV to finish exploring the assigned area. We use the particle swarm optimization (PSO) method to compute the optimal region partitions. The method is verified by running simulations in different test environments. We also analyze the performance of the developed method in environments where speed restrictions are not known in advance.

Commentary by Dr. Valentin Fuster