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### Research Papers

J. Mechanisms Robotics. 2017;9(6):061001-061001-7. doi:10.1115/1.4037619.

The paper presents a simple and effective kinematic model and methodology to assess and evaluate the extent of the position uncertainty caused by joint clearances for multiple-loop linkage and manipulators connected with revolute or prismatic pairs. The model is derived and explained with geometric rigor based on Ting's rotatability laws.ff2 The significant contributions include (1) the clearance link model for a P-joint that catches the translation and oscillation characteristics of the slider within the clearance and separates the geometric effect of clearances from the input error, (2) the generality of the method, which is effective for multiloop linkages and parallel manipulators, and (3) settling the dispute on the position uncertainty effect to parallel and serial robots due to joint clearance. The discussion is illustrated and carried out through symmetrically configured planar 8 bar parallel robots. It is found that at a target position, the uncertainty region of a three degrees-of-freedom (DOF) three-leg parallel robot is enclosed by a hexagon with curve edges, while that of its serial counterpart is enclosed by a circle included in the hexagon. A numerical example is presented. The finding and proof, though only based on three-leg planar 8 bar parallel robots, may have a wider implication suggesting that based on the kinematic effect of joint clearance, parallel robots tends to inherit more position uncertainty than their serial counterparts. The use of more loops in not only parallel robots but also single-DOF linkages cannot fully offset the adverse effect on position uncertainty caused by the use of more joints.

Commentary by Dr. Valentin Fuster
J. Mechanisms Robotics. 2017;9(6):061002-061002-11. doi:10.1115/1.4037567.

Space robots require compact joint drive systems (JDSs), typically comprising of actuator, transmission, joint elements that can deliver high torques through stiff mechanical ports. Today's conventional space drive systems are made from off-the-shelf actuators and multistage transmissions that generally involve three to six stages. This current practice has certain benefits such as short development time due to the availability of mechanical components. However, it lacks a system-level integration that accounts for the actuator structure, size and output force, transmission structure, gear-ratio, and strength, and often leads to long and bulky assemblies with large number of parts. This paper presents a new robotic hardware that integrates the robot's JDS into one compact device that is optimized for its size and maximum torque density. This is done by designing the robotic joint using a special transmission which, when numerically optimized, can produce unlimited gear-ratios using only two stages. The design is computerized to obtain all the solutions that satisfy its kinematic relationships within a given actuator diameter. Compared to existing robotic actuators, the proposed design could lead to shorter assemblies with significantly lower number of parts for the same output torque. The theoretical results demonstrates the potential of an example device, for which a proof-of-concept plastic mockup was fabricated, that could deliver more than 200 N·m of torque in a package as small as a human elbow joint. The proposed technology could have strong technological implications in other industries such as powered prosthetics and rehabilitation equipment.

Commentary by Dr. Valentin Fuster
J. Mechanisms Robotics. 2017;9(6):061003-061003-9. doi:10.1115/1.4037616.

A gravity equilibrator is a statically balanced system which is designed to counterbalance a mass such that any preferred position is eliminated and thereby the required operating effort to move the mass is greatly reduced. Current spring-to-mass gravity equilibrators are limited in their range of motion as a result of constructional limitations. An increment of the range of motion is desired to expand the field of applications. The goal of this paper is to present a compact one degree-of-freedom mechanical gravity equilibrator that can statically balance a rotating pendulum over an unlimited range of motion. Static balance over an unlimited range of motion is achieved by a coaxial gear train that uses noncircular gears. These gears convert the continuous rotation of the pendulum into a reciprocating rotation of the torsion bars. The pitch curves of the noncircular gears are specifically designed to balance a rotating pendulum. The gear train design and the method to calculate the parameters and the pitch curves of the noncircular gears are presented. A prototype is designed and built to validate that the presented method can balance a pendulum over an unlimited range of motion. Experimental results show a work reduction of 87% compared to an unbalanced pendulum and the hysteresis in the mechanism is 36%.

Commentary by Dr. Valentin Fuster
J. Mechanisms Robotics. 2017;9(6):061004-061004-10. doi:10.1115/1.4037800.

This paper proposes a two translational and two rotational (2T2R) four-degrees-of-freedom (DOF) parallel kinematic mechanism (PKM) designed as a knee rehabilitation and diagnosis mechatronics system. First, we establish why rehabilitation devices with 2T2R motion are required, and then, we review previously proposed parallel mechanisms with this type of motion. After that, we develop a novel proposal based on the analysis of each kinematic chain and the Grübler–Kutzbach criterion. Consequently, the proposal consists of a central limb with revolute-prismatic-universal (RPU) joints and three external limbs with universal-prismatic-spherical (UPS) joints. The Screw theory analysis verifies the required mobility of the mechanism. Also, closed-loop equations enable us to put forward the closed-form solution for the inverse-displacement model, and a numerical solution for the forward-displacement model. A comparison of the numerical results from five test trajectories and the solution obtained using a virtual prototype built in msc-adams shows that the kinematic model represents the mechanism's motion. The analysis of the forward-displacement problem highlights the fact that the limbs of the mechanism should be arranged asymmetrically. Moreover, the Screw theory makes it possible to obtain the Jacobian matrix which provides insights into the analysis of the mechanism's workspace. The results show that the proposed PKM can cope with the required diagnosis and rehabilitation task. The results provide the guidelines to build a first prototype of the mechanism which enables us to perform initial tests on the robot.

Commentary by Dr. Valentin Fuster
J. Mechanisms Robotics. 2017;9(6):061005-061005-9. doi:10.1115/1.4037801.

The classic Burmester problem is concerned with computing dimensions of planar four-bar linkages consisting of all revolute joints for five-pose problems. We define extended Burmester problem as the one where all types of planar four-bars consisting of dyads of type RR, PR, RP, or PP (R: revolute, P: prismatic) and their dimensions need to be computed for n-geometric constraints, where a geometric constraint is an algebraically expressed constraint on the pose, pivots, or something equivalent. In addition, we extend it to linear, nonlinear, exact, and approximate constraints. This extension also includes the problems when there is no solution to the classic Burmester problem, but designers would still like to design a four-bar that may come closest to capturing their intent. Machine designers often grapple with such problems while designing linkage systems where the constraints are of different varieties and usually imprecise. In this paper, we present (1) a unified approach for solving the extended Burmester problem by showing that all linear and nonlinear constraints can be handled in a unified way without resorting to special cases, (2) in the event of no or unsatisfactory solutions to the synthesis problem, certain constraints can be relaxed, and (3) such constraints can be approximately satisfied by minimizing the algebraic fitting error using Lagrange multiplier method. We present a new algorithm, which solves new problems including optimal approximate synthesis of Burmester problem with no exact solutions.

Commentary by Dr. Valentin Fuster
J. Mechanisms Robotics. 2017;9(6):061006-061006-12. doi:10.1115/1.4037802.

This paper examines the dynamics of a type of silicon-based millimeter-scale hexapod, focusing on interaction between structural dynamics and ground contact forces. These microrobots, having a 5 mm × 2 mm footprint, are formed from silicon with integrated thin-film lead–zirconate–titanate (PZT) and high-aspect-ratio parylene-C polymer microactuation elements. The in-chip dynamics of the microrobots are measured when actuated with tethered electrical signal to characterize the resonant behavior of different parts of the robot and its piezoelectric actuation. Out-of-chip robot motion is then stimulated by external vibration after the robot has been detached from its silicon tethers, which removes access to external power but permits sustained translation over a surface. A dynamic model for robot and ground interaction is presented to explain robot locomotion in the vibrating field using the in-chip measurements of actuator dynamics and additional dynamic properties obtained from finite element analysis (FEA) and other design information. The model accounts for the microscale interaction between the robot and ground, for multiple resonances of the robot leg, and for rigid robot body motion of the robot chassis in five degrees-of-freedom. For each mode, the motions in vertical and lateral direction are coupled. Simulation of this dynamic model with the first three resonant modes (one predominantly lateral and two predominantly vertical) of each leg shows a good match with experimental results for the motion of the robot on a vibrating surface, and allows exploration of influence of small-scale forces such as adhesion on robot locomotion. Further predictions for future autonomous microrobot performance based on the dynamic phenomena observed are discussed.

Commentary by Dr. Valentin Fuster
J. Mechanisms Robotics. 2017;9(6):061007-061007-12. doi:10.1115/1.4037805.

Two kinds of mechanical redundancies, namely kinematic redundancy and actuation redundancy, have been extensively studied due to their advantageous features in autonomous industry. Screw theory has been successfully applied to develop an analytical Jacobian of nonredundant parallel manipulators (PMs). However, to the best of our knowledge, screw theory has not been attempted for modeling of PMs with kinematic redundancies. Thus, first, through the mobility analysis of a simple nonredundant planar PM and its variations, this paper reviews kinematic and actuation redundancy systematically. Then, we demonstrated how to derive analytical Jacobian and also static force relationship for a PM with both kinematic and actuation redundancies by using the screw theory. Finally, simulations were performed to demonstrate the advantageous features of kinematic and actuation redundancies.

Commentary by Dr. Valentin Fuster
J. Mechanisms Robotics. 2017;9(6):061008-061008-11. doi:10.1115/1.4037892.

The paper presents a theory of vibratory locomotion, a prototype, and the results of experiments on mini robot, which moves as a result of inertial excitation provided by two electric motors. The robot is equipped with elastic bristles which are in contact with the supporting surface. Vibration of the robot generates the friction force which can push the robot forward or backward. The paper presents a novel model of interaction between the bristles and the supporting surface. The friction force (its magnitude and sense) is defined as a function of the robot velocity and the robot's vibrations. The analysis is done for a constant coefficient of friction and a smooth surface. Depending on the motors' speed, one may obtain a rectilinear or a curvilinear motion, without jumping or losing contact with the substrate. The results of the simulation show which way the robot moves, its mean velocity of locomotion, change of the slipping velocity of the bristles and its influence on the normal and the friction force. A prototype was built and experiments were performed with it.

Topics: Robots , Friction , Vibration
Commentary by Dr. Valentin Fuster
J. Mechanisms Robotics. 2017;9(6):061009-061009-9. doi:10.1115/1.4037803.

For under-constrained and redundant parallel manipulators, the actuator inputs are studied with bounded variations in parameters and data. Problem is formulated within the context of force analysis. Discrete and analytical methods for interval linear systems are presented, categorized, and implemented to identify the solution set, as well as the minimum 2-norm least-squares solution set. The notions of parameter dependency and solution subsets are considered. The hyperplanes that bound the solution in each orthant characterize the solution set of manipulators. While the parameterized form of the interval entries of the Jacobian matrix and wrench produce the minimum 2-norm least-squares solution for the under-constrained and over-constrained systems of real matrices and vectors within the interval Jacobian matrix and wrench vector, respectively. Example manipulators are used to present the application of methods for identifying the solution and minimum norm solution sets for actuator forces/torques.

Commentary by Dr. Valentin Fuster
J. Mechanisms Robotics. 2017;9(6):061010-061010-11. doi:10.1115/1.4037760.

This paper is focused on design of dive maneuvers that can be performed outdoors on flapping wing air vehicles (FWAVs) with a minimal amount of on-board computing capability. We present a simple computational model that provides accuracy of 5 m in open loop operation mode for outdoor dives under wind speeds of up to 3 m/s. This model is executed using a low power, on-board processor. We have also demonstrated that the platform can independently execute roll control through tail positioning, and dive control through wing positioning to produce safe dive behaviors. These capabilities were used to successfully demonstrate autonomous dive maneuvers on the Robo Raven platform developed at the University of Maryland.

Commentary by Dr. Valentin Fuster
J. Mechanisms Robotics. 2017;9(6):061011-061011-9. doi:10.1115/1.4038010.

This paper presents the design, simulation, fabrication, and testing processes of a new microelectromechanical systems (MEMS) microgripper, which integrates an electrostatic actuator and a capacitive force sensor. One advantage of the presented gripper is that the gripping force and interaction force in two orthogonal directions can be, respectively, detected by a single force sensor. The whole gripper structure consists of the left actuating part and right sensing part. It owns a simple structure and compact footprint. The actuator and sensor are fixed and linearly guided by four leaf flexures, respectively. The left arm of the gripper is driven through a lever amplification mechanism. By this structure, the displacement from the electrostatic actuator is transmitted and enlarged at the gripper tip. The right arm of the gripper is designed to detect the gripping and interaction forces using a capacitive sensor. The MEMS gripper is manufactured by SOIMUMPs process. The performance of the designed gripper is verified by conducting finite element analysis (FEA) simulation and experimental studies. Moreover, the demonstration of biocellulose gripping confirms the feasibility of the developed gripper device.

Commentary by Dr. Valentin Fuster
J. Mechanisms Robotics. 2017;9(6):061012-061012-11. doi:10.1115/1.4038009.

This paper presents a design procedure for a two degree-of-freedom (DOF) translational parallel manipulator, named IRSBot-2. This design procedure aims at determining the optimal design parameters of the IRSBot-2 such that the robot can reach a velocity equal to 6 m/s, an acceleration up to 20 G, and a multidirectional repeatability up to 20 μm throughout its operational workspace. Besides, contrary to its counterparts, the stiffness of the IRSBot-2 should be very high along the normal to the plane of motion of its moving platform. A semi-industrial prototype of the IRSBot-2 has been realized based on the obtained optimum design parameters. This prototype and its main components are described in the paper. Its accuracy, repeatability, elasto-static performance, dynamic performance, and elasto-dynamic performance have been measured and analyzed as well. It turns out that the IRSBot-2 has globally reached the prescribed specifications and is a good candidate to perform very fast and accurate pick-and-place operations.

Commentary by Dr. Valentin Fuster
J. Mechanisms Robotics. 2017;9(6):061013-061013-10. doi:10.1115/1.4038007.

This paper develops an approach to evaluate a state-space controller design for mobile manipulators using a geometric representation of the system response in tool space. The method evaluates the robot system dynamics with a control scheme and the resulting response is called the controllability ellipsoid (CE), a tool space representation of the system’s motion response given a unit input. The CE can be compared with a corresponding geometric representation of the required motion task (called the motion polyhedron) and evaluated using a quantitative measure of the degree to which the task is satisfied. The traditional control design approach views the system response in the time domain. Alternatively, the proposed CE views the system response in the domain of the input variables. In order to complete the task, the CE must fully contain the motion polyhedron. The optimal robot arrangement would minimize the total area of the CE while fully containing the motion polyhedron. This is comparable to minimizing the power requirements of robot design when applying a uniform scale to all inputs. It will be shown that changing the control parameters changes the eccentricity and orientation of the CE, implying a preferred set of control parameters to minimize the design motor power. When viewed in the time domain, the control parameters can be selected to achieve desired stability and time response. When coupled with existing control design methods, the CE approach can yield robot designs that are stable, responsive, and minimize the input power requirements.

Commentary by Dr. Valentin Fuster
J. Mechanisms Robotics. 2017;9(6):061014-061014-14. doi:10.1115/1.4038068.

In this paper, dynamic modeling of cable-driven parallel robots (CDPRs) is addressed where each cable length is subjected to variations during operation. It is focusing on an original formulation of cable tension, which reveals a softening behavior when strains become large. The dynamic modulus of cable elasticity is experimentally identified through dynamic mechanical analysis (DMA). Numerical investigations carried out on suspended CDPRs with different sizes show the effect of the proposed tension formulation on the dynamic response of the end-effector.

Commentary by Dr. Valentin Fuster
J. Mechanisms Robotics. 2017;9(6):061015-061015-6. doi:10.1115/1.4038008.

Principles from origami art are applied in the design of mechanisms and robotics increasingly frequent. A large part of the application driven research of these origami-like mechanisms focuses on devices where the creases (hinge lines) are actuated and the facets are constructed as stiff elements. In this paper, a design tool is proposed in which hinge lines with torsional stiffness and flexible facets are used to design passive, instead of active mechanisms. The design tool is an extension of a model of a single vertex compliant facet origami mechanism (SV-COFOM) and is used to approximate a desired moment curve by optimizing the design variables of the mechanism. Three example designs are presented: a constant moment joint (CMJ), a gravity compensating joint (GCJ) and a zero moment joint (ZMJ). The CMJ design has been evaluated experimentally, resulting in a root-mean-squared error (RMSE) of 6.4 × 10−2 N·m on a constant moment value of 0.39 N·m. This indicates that the design tool is suitable for a course estimation of the moment curve of the SV-COFOM in early stages of a design process.

Topics: Hinges , Design , Stiffness
Commentary by Dr. Valentin Fuster
J. Mechanisms Robotics. 2017;9(6):061016-061016-11. doi:10.1115/1.4038065.

This paper aims to construct a novel family of deployable mechanisms from a class of two-layer and two-loop spatial linkages, each of which consists of an eight revolute pair (8R) single-loop linkage connected by a 5R serial chain. First, structural characteristics of the class of linkages as deployable units are analyzed and illustrated. Then, the two-layer and two-loop spatial linkages with 5R chains satisfying the structural characteristics are systematically synthesized. Mobile assembly modes between deployable units are established based on degree-of-freedom (DOF) analysis. Finally, a family of single DOF deployable mechanisms is constructed based on the synthesized deployable units and the established assembly modes. The derived deployable mechanisms have the characteristic of the umbrella-like structure, and they have various mesh shapes, which can meet different kinds of application requirements.

Commentary by Dr. Valentin Fuster
J. Mechanisms Robotics. 2017;9(6):061017-061017-13. doi:10.1115/1.4038217.

This paper presents a novel fingertip system with a two-layer structure for robotic hands. The outer part of the structure consists of a rubber bag filled with fluid, called the “fluid fingertip,” while the inner part consists of a rigid link mechanism called a “microgripper.” The fingertip thus is a rigid/fluid hybrid system. The fluid fingertip is effective for grasping delicate objects, that is, it can decrease the impulsive force upon contact, and absorb uncertainties in object shapes and contact force. However, it can only apply a small grasping force such that holding a heavy object with a robotic hand with fluid fingertips is difficult. Additionally, contact uncertainties including inaccuracies in the contact position control cannot be avoided. In contrast, rigid fingertips can apply considerable grasping forces and thus grasp heavy objects effectively, although this makes delicate grasping difficult. To maintain the benefits of the fluid fingertip while overcoming its disadvantages, the present study examines passively operable microgripper-embedded fluid fingertips. Our goal is to use the gripper to enhance the positioning accuracy and increase the grasping force by adding geometrical constraints to the existing mechanical constraints. Grasping tests showed that the gripper with the developed fingertips can grasp a wide variety of objects, both fragile and heavy.

Commentary by Dr. Valentin Fuster

### Technical Brief

J. Mechanisms Robotics. 2017;9(6):064501-064501-5. doi:10.1115/1.4038066.

A general optimization model for the dimensional synthesis of defect-free revolute-cylindrical-cylindrical-cylindrical joint (or RCCC) motion generators is formulated and demonstrated in this work. With this optimization model, the RCCC dimensions required to approximate an indefinite number of precision positions are calculated. The model includes constraints to eliminate order branch and circuit defects—defects that are common in dyad-based dimensional synthesis. Therefore, the novelty of this work is the development of a general optimization model for RCCC motion generation for an indefinite number of precision positions that simultaneously considers order, branch, and circuit defect elimination. This work conveys both the benefits and drawbacks realized when implementing the optimization model on a personal computer using the commercial mathematical analysis software package matlab.

Commentary by Dr. Valentin Fuster
J. Mechanisms Robotics. 2017;9(6):064502-064502-6. doi:10.1115/1.4038067.

This paper presents an original Hexacopter with three nonplanar rotor pairs where the variable thrust is provided by fixed-pitch rotors with variable speed. The corresponding face-to-face rotor pair (F–F) and back-to-back rotor pair (B–B) are proposed as the research components to maximize the overall aerodynamic performance with different transverse spacings and disk plane angles. Together with the rotor interactions involved in low Reynolds number (Re) environments, experiments in the presence of the uncertainty analysis are performed to validate the aerodynamic interference and test the effectiveness of the proposed rotor pairs. Experimental results show that the performance of the rotor pair can be improved significantly by having an optimal combination with a larger angle and a moderate spacing. Indeed, the aerodynamic interactions between the two rotors decrease with a larger disk plane angle, and the aerodynamic interference of the rotor pairs is mainly involved in the face to face type. Furthermore, parametric studies were also performed to study the effects of low Re and to attempt to maximize the thrust and minimize the total power required in hover flight. Useful conclusions are provided for the further aerodynamic analysis and control strategy to meet design requirements.

Commentary by Dr. Valentin Fuster

### Errata

J. Mechanisms Robotics. 2017;9(6):067001-067001-1. doi:10.1115/1.4037804.

Table 1 lists some example homotopy startpoints and endpoints. Although the “Roots obtained” in Table 1 are valid solutions of the target system, they do not correspond with the printed “Startpoints” and “Start system parameters” when a homotopy is constructed with the γ parameter listed in the caption. Corrected endpoints are given below: Roots obtainedA−0.066434 + 0.493276i0.202459 + 0.108111i1.198517 − 0.787550iB0.627677 − 0.273186i0.305923 + 0.876130i0.291467 + 1.479257iC0.116929 + 0.972660i −0.466634 + 0.714604i2.675716 − 2.047980iD1.040373 − 0.423983i0.197730 + 0.058068i0.006718 + 1.036395i$A¯$0.262110 + 0.023383i0.632810 + 0.098983i0.747365 + 0.100705i$B¯$0.379733 − 0.030149i −3.436140 + 1.096621i0.222721 + 0.277870i$C¯$0.725885 + 0.357931i0.869835 + 0.314313i0.912556 + 0.232407i$D¯$0.472868 + 0.468932i0.716403 + 0.362794i0.929620 + 0.213314i

Commentary by Dr. Valentin Fuster