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IN THIS ISSUE

### Research Papers

J. Mechanisms Robotics. 2016;8(6):061001-061001-7. doi:10.1115/1.4032862.

Compliant mechanisms achieve motion utilizing deformation of elastic members. However, analysis of compliant mechanisms for large deflections remains a significant challenge. In this paper, a three-spring revolute–prismatic–revolute (RPR) pseudorigid-body (PRB) model for short beams used in soft joints made of elastomer material is presented. These soft joints differ from flexure-based compliant joints in which they demonstrate significant axial elongation effects upon tip loadings. The traditional PRB models based on long thin Euler beams failed to capture this elongation effect. To overcome this difficulty, a model approximation based on the Timoshenko beam theory has been derived. These equations are utilized to calculate the tip deflection for a large range of loading conditions. An optimization process is then carried out to determine the optimal values of the parameters of the PRB model for a large range of tip loads. An example based on a robotic grasper finger is provided to demonstrate how the model can be used in analysis of such a system. This model will provide a simple approach for the analysis of compliant robotic mechanisms.

Commentary by Dr. Valentin Fuster
J. Mechanisms Robotics. 2016;8(6):061002-061002-13. doi:10.1115/1.4033666.

This paper presents a systematic solution of the kinematics of the planar mechanism from the aspect of Assur groups. When the planar mechanism is decomposed into Assur groups, the detailed calculating order of Assur groups is unknown. To solve this problem, first, the decomposed Assur groups are classified into three types according to their calculability, which lays the foundation for the establishment of the automatic solving algorithm for decomposed Assur groups. Second, the data structure for the Assur group is presented, which enables the automatic solving algorithm with the input and output parameters of each Assur group. All decomposed Assur groups are stored in the component stack, and all parameters of which are stored in the parameter stacks. The automatic algorithm will detect identification flags of each Assur group in the component stack and their corresponding parameters in the parameter stacks in order to decide which Assur group is calculable and which one can be solved afterward. The proposed systematic solution is able to generate an automatic solving order for all Assur groups in the planar mechanism and allows the adding, modifying, and removing of Assur groups at any time. Two planar mechanisms are given as examples to show the detailed process of the proposed systematic solution.

Commentary by Dr. Valentin Fuster
J. Mechanisms Robotics. 2016;8(6):061003-061003-8. doi:10.1115/1.4033434.

This paper deals with the problem of integrated joint type and dimensional synthesis of planar four-bar and six-bar linkages, which could contain both revolute (R) and prismatic (P) joints, for guiding through five specified task positions of the end-effector. In a recent work, we developed a simple algorithm for analyzing a set of given task positions to determine all feasible planar dyads with revolute and/or prismatic joints that can be used to guide through the given positions. This paper extends this algorithm to the integrated joint type and dimensional synthesis of Watt I and II and Stephenson I, II, and III six-bar linkages that contain both R- and P-joints. In the process, we developed a new classification for planar six-bar linkages according to whether the end-effector can be constrained by two dyads (type I), one dyad (type II), or no dyad (type III). In the end, we demonstrate this task-driven synthesis approach with three examples including a novel six-bar linkage for lifting an individual with age disability from seating position to standing position.

Commentary by Dr. Valentin Fuster
J. Mechanisms Robotics. 2016;8(6):061004-061004-9. doi:10.1115/1.4033667.

This paper analyzes the dynamics of robotic manipulator based on a concept called dynamic reconfiguration manipulability (DRM), which gauges the dynamical shape-changeability of a robot based on the redundancy of the robot and the premise that the primary task is the hand task. DRM represents how much acceleration each intermediate link can generate and in what direction the acceleration can be realized based on normalized torque inputs. This concept will aid in the optimization of the design and control of robots. The appropriateness and usefulness of DRM were confirmed by applying it to redundant manipulators and comparing it with the known concept of avoidance manipulability.

Commentary by Dr. Valentin Fuster
J. Mechanisms Robotics. 2016;8(6):061005-061005-9. doi:10.1115/1.4032408.

A manipulator control system, for which isotropic compliance holds in the Euclidean space $E(3)$, can be significantly simplified by means of diagonal decoupling. However, such simplification may introduce some limits to the region of the workspace where the sought property can be achieved. The present investigation reveals how to detect which peculiar subset, among four different classes, a given manipulator belongs to. The paper also introduces the concept of control gain ratio for each specific single-input/single-output joint control law in order to limit the maximum gain required to achieve the isotropic compliance condition.

Topics: Manipulators
Commentary by Dr. Valentin Fuster
J. Mechanisms Robotics. 2016;8(6):061006-061006-9. doi:10.1115/1.4033695.

Designing an effective cable architecture for a cable-driven robot becomes challenging as the number of cables and degrees of freedom of the robot increase. A methodology has been previously developed to identify the optimal design of a cable-driven robot for a given task using stochastic optimization. This approach is effective in providing an optimal solution for robots with high-dimension design spaces, but does not provide insights into the robustness of the optimal solution to errors in the configuration parameters that arise in the implementation of a design. In this work, a methodology is developed to analyze the robustness of the performance of an optimal design to changes in the configuration parameters. This robustness analysis can be used to inform the implementation of the optimal design into a robot while taking into account the precision and tolerances of the implementation. An optimized cable-driven robot leg is used as a motivating example to illustrate the application of the configuration robustness analysis. Following the methodology, the effect on robot performance due to design variations is analyzed, and a modified design is developed which minimizes the potential performance degradations due to implementation errors in the design parameters. A robot leg is constructed and is used to validate the robustness analysis by demonstrating the predicted effects of variations in the design parameters on the performance of the robot.

Commentary by Dr. Valentin Fuster
J. Mechanisms Robotics. 2016;8(6):061007-061007-14. doi:10.1115/1.4033855.

A method for optimizing a mobile platform to form a wheeled manipulator is presented. For a given manipulator, this mobile platform is optimized to have maximum tip-over stability against the reaction forces and moments caused by the movement of the manipulator. This optimization is formulated as a max–min problem, i.e., to maximize a stable region ratio (SRR) over the manipulator's workspace while minimizing a tip-over moment (TOM). For a practical solution, this max–min problem is converted to two subproblems. The first one is the worst-case analysis to determine the maximum positive value of TOM through searching over the manipulator's workspace. A positive value of TOM indicates tip-over instability. The three parameters used for this search are pertaining to the mobile platform itself, i.e., the number of support wheels, the size, and mass of the mobile platform. The second subproblem is to optimize the placement of the manipulator and accessory on the mobile platform against the identified worst case so that the entire manipulator's workspace is stable. The effectiveness of the proposed method is demonstrated by applying it to optimize a mobile drilling and riveting robot.

Commentary by Dr. Valentin Fuster
J. Mechanisms Robotics. 2016;8(6):061008-061008-10. doi:10.1115/1.4034142.

Variable stiffness actuators (VSAs) can improve the robot's performance during interactions with human and uncertain environments. Based on the modified gear–rack mechanism, a VSA with a third-power stiffness profile is designed. The proposed mechanism, used to vary the joint stiffness, is placed between the output end and the joint speed reducer. Both the elastic element and the regulating mechanism are combined into the modified gear–rack (MGR), which is modeled as an elastic beam clamped at the middle position. Two pairs of spur gears are engaged with the rack and considered as the variable acting positions of supporting forces. The joint stiffness is inversely proportional to the third power of the gear displacement, independent from the joint position and the joint deflection angle. The gear displacement is perpendicular to the loading torque, so the power consumed by the stiffness-regulating action is low (14.4 W). The working principle and the mechanics model are illustrated, and then, the mechanical design is presented. The validity of the VSA is proved by simulations and experiments.

Topics: Stiffness , Deflection , Gears
Commentary by Dr. Valentin Fuster
J. Mechanisms Robotics. 2016;8(6):061009-061009-7. doi:10.1115/1.4034141.

This paper presents a synthesis method for the Stephenson III six-bar linkage that combines the direct solution of the synthesis equations with an optimization strategy to achieve increased performance for path generation. The path synthesis equations for a six-bar linkage can reach as many as 15 points on a curve; however, the degree of the polynomial system is 1046. In order to increase the number of accuracy points and decrease the complexity of the synthesis equations, a new formulation is used that combines 11 point synthesis with optimization techniques to obtain a six-bar linkage that minimizes the distance to 60 accuracy points. This homotopy directed optimization technique is demonstrated by obtaining a Stephenson III six-bar linkage that achieves a specified gait trajectory.

Commentary by Dr. Valentin Fuster
J. Mechanisms Robotics. 2016;8(6):061010-061010-15. doi:10.1115/1.4033728.

In this paper, a novel robotic gripper design with variable stiffness is proposed and fabricated using a modified additive manufacturing (hereafter called 3D printing) process. The gripper is composed of two identical robotic fingers and each finger has three rotational degrees-of-freedom as inspired by human fingers. The finger design is composed of two materials: acrylonitrile butadiene styrene (ABS) for the bone segments and shape-memory polymer (SMP) for the finger joints. When the SMP joints are exposed to thermal energy and heated to above their glass transition temperature (Tg), the finger joints exhibit very small stiffness, thus allow easy bending by an external force. When there is no bending force, the finger will restore to its original shape thanks to SMP's shape recovering stress. The finger design is actuated by a pneumatics soft actuator. Fabrication of the proposed robotic finger is made possible by a modified 3D printing process. An analytical model is developed to represent the relationship between the soft actuator's air pressure and the finger's deflection angle. Furthermore, analytical modeling of the finger stiffness modulation is presented. Several experiments are conducted to validate the analytical models.

Commentary by Dr. Valentin Fuster
J. Mechanisms Robotics. 2016;8(6):061011-061011-9. doi:10.1115/1.4033665.

In this paper, a method for the optimal design of metamorphic manipulators is presented, using path dexterity indices in diverse service tasks. The Swedish massage service is chosen as an application, due the very dissimilar techniques that can be challenging for fixed anatomy manipulators. These techniques are presented and a mapping to dexterity indices is proposed based on each technique's requirements. A method for the evaluation of metamorphic anatomies over tasks is proposed, and the optimized anatomy of a metamorphic manipulator is determined. Finally, an illustrative example is presented for three tasks, where the advantages of the anatomy optimization are demonstrated.

Commentary by Dr. Valentin Fuster
J. Mechanisms Robotics. 2016;8(6):061012-061012-11. doi:10.1115/1.4033859.

Mobility analysis is an important step in the conceptual design of flexure systems. It involves identifying directions with relatively compliant motion (freedoms) and directions with relatively restricted motion (constraints). This paper proposes a deterministic framework for mobility analysis of wire flexure systems based on characterizing a kinetostatic vector field known as “load flow” through the geometry. A hypothesis is proposed to identify constraints and freedoms based on the relationship between load flow and the flexure geometry. This hypothesis is mathematically restated to formulate a matrix-based reduction technique that determines flexure mobility computationally. Several examples with varying complexity are illustrated to validate the efficacy of this technique. This technique is particularly useful in analyzing complex hybrid interconnected flexure topologies, which may be nonintuitive or involved with traditional methods. This is illustrated through the computational mobility analysis of a bio-inspired fiber reinforced elastomer pressurized with fluids. The proposed framework combines both visual insight and analytical rigor, and will complement existing analysis and synthesis techniques.

Commentary by Dr. Valentin Fuster
J. Mechanisms Robotics. 2016;8(6):061013-061013-8. doi:10.1115/1.4034015.

This article details the design, fabrication, and application of a mechatronic arm exoskeleton for firearm aim stabilization (MAXFAS), which senses and damps involuntary tremors in the arm. Human subject experiments were carried out using the device in a simulated shooting and aiming task. Results indicate that MAXFAS reduced arm tremors and improved shooting performance while wearing the device. Residual performance improvement after removing the device and possible training function of MAXFAS will also be discussed.

Commentary by Dr. Valentin Fuster
J. Mechanisms Robotics. 2016;8(6):061014-061014-9. doi:10.1115/1.4034014.

This paper presents the design and integration of a genderless coupling mechanism for modular self-reconfigurable mobile robots. Modular self-reconfigurable mobile robotic systems consist of a number of self-sufficient modules that interconnect via coupling mechanisms and adopt different configurations to modify locomotion and/or manipulation capabilities. Coupling mechanisms are a critical element of these robotic systems. This paper focuses on a docking mechanism called GHEFT: a Genderless, High-strength, Efficient, Fail-safe, and high misalignment Tolerant coupling mechanism that aids self-reconfiguration. GHEFT provides a high strength and energy efficient connection using nonback drivable actuation with optimized clamping profiles that tolerate translational and angular misalignments. It also enables engagement/disengagement without gender restrictions in the presence of one-sided malfunction. The detailed design of the proposed mechanism is presented, including optimization of the clamping profile geometries. Experimental validation of misalignment tolerances and achievable clamping forces and torques is performed to demonstrate the strength, efficiency, and fail-safe capabilities of the proposed mechanism, and these results are compared to reported results of some of the existing coupling mechanisms.

Topics: Robots , Design , Torque , Simulation
Commentary by Dr. Valentin Fuster
J. Mechanisms Robotics. 2016;8(6):061015-061015-10. doi:10.1115/1.4034464.

This paper investigates the influence of the load connection form on the walking energetics and kinetics with simple models. Four load connection forms including rigid connection (RIC), springy connection (SPC), swingy connection (SWC), and springy and swingy connection (SSC) were modeled. The step-to-step transition of periodic walking was studied through an analytical method. The toe-off impulse magnitude and the work done by toe-off were derived. Simulations were performed to study the walking performance of each model and the effect of model parameters on the gait properties. The analysis and simulation results showed that compared with RIC, SPC and SSC can significantly improve the toe-off efficiency and change the ground reaction force (GRF) profile by reducing the burden during the step-to-step transition, which may lead to reduction of walking energy cost. Energetics and kinetics of SWC are closely related to the swing angle of load at the transition moment. The load swing may decrease the walking speed, and it is not beneficial to walking efficiency.

Commentary by Dr. Valentin Fuster
J. Mechanisms Robotics. 2016;8(6):061016-061016-10. doi:10.1115/1.4034577.

Manufacturing and assembly (geometric) errors affect the positioning precision of manipulators. In six degrees-of-freedom (6DOF) manipulators, geometric error effects can be compensated through suitable calibration procedures. This, in general, is not possible in lower-mobility manipulators. Thus, methods that evaluate such effects must be implemented at the design stage to determine both which workspace region is less affected by these errors and which dimensional tolerances must be assigned to match given positioning-precision requirements. In the literature, such evaluations are mainly tailored on particular architectures, and the proposed techniques are difficult to extend. Here, a general discussion on how to take into account geometric error effects is presented together with a general method to solve this design problem. The proposed method can be applied to any nonoverconstrained architecture. Eventually, as a case study, the method is applied to the analysis of the geometric error effects of the translational parallel manipulator (TPM) Triflex-II.

Commentary by Dr. Valentin Fuster
J. Mechanisms Robotics. 2016;8(6):061017-061017-10. doi:10.1115/1.4034143.

Surgical procedures are traditionally performed by two or more surgeons along with staff nurses: one serves as the primary surgeon and the other as his/her assistant. Introducing surgical robots into the operating room has significantly changed the dynamics of interaction between the surgeons and with the surgical site. In this paper, we design a surgical robotic system to support the collaborative operation of multiple surgeons. This Raven IV surgical robotic system has two pairs of articulated robotic arms with a spherical configuration, each arm holding an articulated surgical tool. It allows two surgeons to teleoperate the Raven IV system collaboratively from two remote sites. To optimize the mechanism design of the Raven IV system, we configure the link architecture of each robotic arm, along with the position and orientation of the four bases and the port placement with respect to the patient's body. The optimization considers seven different parameters, which results in $2.3×1010$ system configurations. We optimize the common workspace and the manipulation dexterity of each robotic arm. We study here the effect of each individual parameter and conduct a brute force search to find the optimal set of parameters. The parameters for the optimized configuration result in an almost circular common workspace with a radius of 150 mm, accessible to all four arms.

Commentary by Dr. Valentin Fuster
J. Mechanisms Robotics. 2016;8(6):061018-061018-9. doi:10.1115/1.4034788.

This paper presents a comprehensive methodology for ensuring the geometric pose accuracy of a 4DOF high-speed pick-and-place parallel robot having an articulated traveling plate. The process is implemented by four steps: (1) formulation of the error model containing all possible geometric source errors; (2) tolerance design of the source errors affecting the uncompensatable pose accuracy via sensitivity analysis; (3) identification of the source errors affecting the compensatable pose accuracy via a simplified model and distance measurements; and (4) development of a linearized error compensator for real-time implementation. Experimental results show that a tilt angular accuracy of 0.1/100 and a volumetric/rotational accuracy of 0.5 mm/±0.8 deg of the end-effector can be achieved over the cylindrical task workspace.

Commentary by Dr. Valentin Fuster
J. Mechanisms Robotics. 2016;8(6):061019-061019-22. doi:10.1115/1.4034299.
OPEN ACCESS

Origami provides both inspiration and potential solutions to the fabrication, assembly, and functionality of various structures and devices. Kinematic modeling of origami-based objects is essential to their analysis and design. Models for rigid origami, in which all planar faces of the sheet are rigid and folds are limited to straight creases having only zeroth-order geometric continuity, are available in the literature. Many of these models include constraints on the fold angles to ensure that any initially closed strip of faces is not torn during folding. However, these previous models are not intended for structures with non-negligible fold thickness or with maximum curvature at the folds restricted by material or structural limitations. Thus, for general structures, creased folds of merely zeroth-order geometric continuity are not appropriate idealizations of structural response, and a new approach is needed. In this work, a novel model analogous to those for rigid origami with creased folds is presented for sheets having realistic folds of nonzero surface area and exhibiting higher-order geometric continuity, here termed smooth folds. The geometry of smooth folds and constraints on their associated shape variables are presented. A numerical implementation of the model allowing for kinematic simulation of sheets having arbitrary fold patterns is also described. Simulation results are provided showing the capability of the model to capture realistic kinematic response of origami sheets with diverse fold patterns.

Commentary by Dr. Valentin Fuster
J. Mechanisms Robotics. 2016;8(6):061020-061020-10. doi:10.1115/1.4034884.

This work is devoted to simplify the inverse–forward kinematics of a parallel manipulator generator of the 3T1R motion. The closure equations of the displacement analysis are formulated based on the coordinates of two points embedded in the moving platform. Afterward, five quadratic equations are solved by means of a novel method based on Gröbner bases endowed with first-order perturbation and local stability of parameters. Meanwhile, the input–output equations of velocity and acceleration are systematically obtained by resorting to reciprocal-screw theory. In that concern, the inclusion of pseudokinematic pairs connecting the limbs to the fixed platform and a passive kinematic chain to the robot manipulator allows to avoid the handling of rank-deficient Jacobian matrices. The workspace of the robot is determined by using a discretized method associated to its inverse–forward displacement analysis, whereas the singularity analysis is approached based on the input–output equation of velocity. Numerical examples are provided with the purpose to show the application of the method.

Commentary by Dr. Valentin Fuster
J. Mechanisms Robotics. 2016;8(6):061021-061021-12. doi:10.1115/1.4034787.

Minimalist, underactuated hand designs can be modified to produce useful, dexterous, in-hand capabilities without sacrificing their passive adaptability in power grasping. Incorporating insight from studies in parallel mechanisms, we implement and investigate the “spherical hand” morphologies: novel, hand topologies with two fingers configured such that the instantaneous screw axes, describing the displacement of the grasped object, always intersect at the same point relative to the palm. This produces the same instantaneous motion about a common point for any object geometry in a stable grasp. Various rotary fingertip designs are also implemented to help maintain stable contact conditions and minimize slip, in order to prove the feasibility of this design in physical hand implementations. The achievable precision manipulation workspaces of the proposed morphologies are evaluated and compared to prior human manipulation data as well as manipulation results with traditional three-finger hand topologies. Experiments suggest that the spherical hands' design modifications can make the system's passive reconfiguration more easily predictable, providing insight into the expected object workspace while minimizing the dependence on accurate object and contact modeling. We believe that this design can significantly reduce the complexity of planning and executing dexterous manipulation movements in unstructured environments with underactuated hands.

Commentary by Dr. Valentin Fuster
J. Mechanisms Robotics. 2016;8(6):061022-061022-10. doi:10.1115/1.4034886.

A spatial parallel kinematic mechanism (PKM) with five degrees of freedom (DoFs) and three limbs is proposed in this paper. To investigate the characteristics of the proposed mechanism's DoFs, mobility analysis based on a line graph method and Grassmann line geometry is carried out. The results show that the mobile platform can rotate about a fixed point at the base and translate in a specific plane (i.e., three rotations and two translations). Therefore, the mobile platform can be located at an arbitrary point in the space and has flexible orientational capability. The orientation of the mobile platform is described by using tilt-and-torsion (T&T) angles, and the kinematics model is established with this precondition. Within the process of kinematics modeling, parasitic motion of the mobile platform is analyzed, and singularity configurations are also disclosed. On this basis, four working modes with different configurations are identified, and one of them is focused on and investigated in detail. The proposed PKM has good potential to be used in the development of movable machine centers. The kinematic analysis is very helpful for the understanding of the concept and the potential applications.

Commentary by Dr. Valentin Fuster

### Technical Brief

J. Mechanisms Robotics. 2016;8(6):064501-064501-5. doi:10.1115/1.4033528.

In an earlier work, we have combined a curve fitting scheme with a type of shape descriptor, Fourier descriptor (FD), to develop a unified method to the synthesis of planar four-bar linkages for generation of both open and closed paths. In this paper, we aim to extend the approach to the synthesis of planar four-bar linkages for motion generation in an FD-based motion fitting scheme. Using FDs, a given motion is represented by two finite harmonic series, one for translational component of the motion and the other for rotational component. It is shown that there is a simple linear relationship between harmonic content of the rotational component and that of the translational component for a planar four-bar coupler motion. Furthermore, it is shown that the rotational component of the given motion identifies a subset of design parameters of a four-bar linkage including link ratios, while the translational component determines the rest of the design parameters such as locations of the fixed pivots. This leads naturally to a decomposed design space for four-bar mechanism synthesis for approximate motion generation.

Commentary by Dr. Valentin Fuster
J. Mechanisms Robotics. 2016;8(6):064502-064502-6. doi:10.1115/1.4034578.

As one new type of deployable structures, foldable plate structures based on origami are more and more widely used in aviation and building structures in recent years. The mobility and kinematic paths of foldable origami structures are studied in this paper. Different constraints including the rigid plate, spherical joints, and the boundary conditions of linkages were first used to generate the system constraint equations. Then, the degree-of-freedom (DOF) of the foldable plate structures was calculated from the dimension of null space of the Jacobian matrix, which is the derivative of the constraint equations with respect to time. Furthermore, the redundant constraints were found by using this method, and multiple kinematic paths existing in origami structures were studied by obtaining all the solutions of constraint equations. Different solutions represent different kinematic configurations. The DOF and kinematic paths of a Miura-ori and a rigid deployable antenna were also investigated in detail.

Commentary by Dr. Valentin Fuster
J. Mechanisms Robotics. 2016;8(6):064503-064503-8. doi:10.1115/1.4034885.

Constant torque compliant mechanisms produce an output torque that does not change in a large range of input rotation. They have wide applications in aerospace, automobile, timing, gardening, medical, and healthcare devices. Unlike constant force compliant mechanisms, the synthesis of constant torque compliant mechanisms has not been extensively investigated yet. In this paper, a method is presented for synthesizing constant torque compliant mechanisms that have coaxial input rotation and output torque. The same shaft is employed for both input rotation and output torque. A synthesized constant torque compliant mechanism is modeled as a set of variable width spline curves within an annular design domain formed between a rotation shaft and a fixed ring. Interpolation circles are used to define variable width spline curves. The synthesis of constant torque compliant mechanisms is systematized as optimizing the control parameters of the interpolation circles of the variable width spline curves. The presented method is demonstrated by the synthesis of constant torque compliant mechanisms that have different number of variable width spline curves in this paper.

Commentary by Dr. Valentin Fuster

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