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IN THIS ISSUE

### Research Papers

J. Mechanisms Robotics. 2015;8(2):021001-021001-8. doi:10.1115/1.4031500.

The paper deals with the evaluation of acceleration of redundant and nonredundant parallel manipulators. The dynamic model of three degrees-of-freedom (3DOF) parallel manipulator is derived by using the virtual work principle. Based on the dynamic model, a measure is proposed for the acceleration evaluation of the redundant parallel manipulator and its nonredundant counterpart. The measure is designed on the basis of the maximum acceleration of the mobile platform when one actuated joint force is unit and other actuated joint forces are less than or equal to a unit force. The measure for evaluation of acceleration can be used to evaluate the acceleration of both redundant parallel manipulators and nonredundant parallel manipulators. Furthermore, the acceleration of the 4-PSS-PU parallel manipulator and its nonredundant counterpart are compared.

Commentary by Dr. Valentin Fuster
J. Mechanisms Robotics. 2015;8(2):021002-021002-6. doi:10.1115/1.4031806.

We use the recently introduced factorization of motion polynomials for constructing overconstrained spatial linkages with a straight-line trajectory. Unlike previous examples of such linkages by other authors, they are single-loop linkages and the end-effector motion is not translational. In particular, we obtain a number of linkages with four revolute and two prismatic joints and a remarkable linkage with seven revolute joints one of whose joints performs a Darboux motion.

Commentary by Dr. Valentin Fuster
J. Mechanisms Robotics. 2015;8(2):021003-021003-7. doi:10.1115/1.4031299.

Optical and magnetic encoders are widely used to measure joint angles. These sensors are required to be installed at the axes of rotation (joint centers). However, microelectromechanical system (MEMS) accelerometer and gyroscope-based joint angle measurement sensors possess the advantage of being flexible with regard to the point of installation. Inertial measurement units (IMUs) are capable of providing orientation and are also used for joint angle estimation. They conventionally fuse gyroscope and accelerometer data using Kalman filter-like algorithm to estimate the joint angles. This research presents a novel approach of measuring joint parameters—joint angles, angular velocities, and accelerations, of two links joined by revolute or universal joint. The gravity-invariant vestibular dynamic inclinometer (VDI) and planar VDI (pVDI) are used on each link to measure the joint parameters of links joined by revolute and universal joints, respectively. The VDI consists of two dual-axis accelerometers and an uniaxial gyroscope, while the pVDI consists of four strategically placed dual-axis accelerometers and a triaxial gyroscope. The measurements of joint parameters using the presented algorithms are independent of integration errors/drift, do not require knowledge of robot dynamics, and are computationally less burdensome.

Commentary by Dr. Valentin Fuster
J. Mechanisms Robotics. 2015;8(2):021004-021004-10. doi:10.1115/1.4031300.

Robotic hands are typically too rigid to react against unexpected impacts and disturbances in order to prevent damage. Human hands have great versatility and robustness due, in part, to the passive compliance at the hand joints. In this paper, we present a novel design for joint with passive compliance that is inspired by biomechanical properties of the human hands. The design consists of a compliant material and a set of pulleys that rotate and stretch the material as the joint rotates. We created six different compliant materials, and we optimized the joint design to match the desired humanlike compliance. We present two design features that allow for the tuning of the joint torque profile, namely, a pretension mechanism to increase pretension of the compliant material, and a design of varying pulley configuration. We built a prototype for the new joint by using additive manufacturing to fabricate the design components and built a test-bed with a force sensor and a servo motor. Experimental results show that the joint exhibits a nonlinear, double exponential joint compliance with all six compliant materials. The design feature involving variable pulley configurations is effective in adjusting the slope of joint torque during the joint rotation while the pretension mechanism showed only a limited effect on increasing the torque amplitude. Overall, with its small size, light weight, low friction, and humanlike joint compliance, the presented joint design is ready for implementation in robotic hands.

Topics: Torque , Design , Pulleys , Robotics
Commentary by Dr. Valentin Fuster
J. Mechanisms Robotics. 2015;8(2):021005-021005-12. doi:10.1115/1.4031192.

There are analytical methods in the literature where a zero-free-length spring-loaded linkage is perfectly statically balanced by addition of more zero-free-length springs. This paper provides a general framework to extend these methods to flexure-based compliant mechanisms through (i) the well know small-length flexure model and (ii) approximation between torsional springs and zero-free-length springs. We use first-order truncated Taylor's series for the approximation between the torsional springs and zero-free-length springs so that the entire framework remains analytical, albeit approximate. Three examples are presented and the effectiveness of the framework is studied by means of finite-element analysis and a prototype. As much as 70% reduction in actuation effort is demonstrated. We also present another application of static balancing of a rigid-body linkage by treating a compliant mechanism as the spring load to a rigid-body linkage.

Commentary by Dr. Valentin Fuster
J. Mechanisms Robotics. 2015;8(2):021006-021006-8. doi:10.1115/1.4031339.

The kinematic synthesis applied to tree topologies is a tool for the design of multifingered robotic hands, for a simultaneous task of all fingertips. Even though traditionally wrists and hands have been designed separately, the wrist usually being part of the robot manipulator arm, it makes sense to consider the wrist as a part of the hand, as many grasping and manipulation actions are a coordinated action of wrist and fingers. The manipulation capabilities of robotic hands may also be enhanced by considering more than one splitting stage, as opposed to the single-palm traditional hand. In this work, we present the dimensional synthesis for a family of multifingered hands, the binary hands, which have a 2R wrist and several splitting stages, each of them spanning two branches consisting of a revolute joint for each edge. For these topologies, it is proved that a three-position task can be defined for each fingertip, regardless of the number of fingers. One example is presented to show the possible design strategies and uses for this family of hands.

Commentary by Dr. Valentin Fuster
J. Mechanisms Robotics. 2015;8(2):021007-021007-9. doi:10.1115/1.4031716.

This article introduces the design and the experimental validation of the Trackhold, a novel mechanical motion-tracker for upper limb physical rehabilitation. The Trackhold is based on a passively balanced mechanism that can approximately relieve the weight of the patient’s arm regardless of the position. The system features a novel kinematic architecture with large workspace and custom developed joint sensors providing accurate real-time measure of the upper limb posture. The design approach of the device, which went through kinetostatic and dynamic analyses, is presented and details on the employed mechatronic solutions are provided. A prototype of the Trackhold has been fabricated and functionally validated.

Commentary by Dr. Valentin Fuster
J. Mechanisms Robotics. 2015;8(2):021008-021008-9. doi:10.1115/1.4031639.

A novel family of deployable mechanisms (DMs) is presented. Unlike most such devices, which have one degree-of-freedom (DOF), the proposed DM can be deployed and compacted independently in two or three directions. This widens the range of its potential applications, including flexible industrial fixtures and deployable tents. The mechanism's basic deployable unit (DU) is assembled by combining a scissor linkage and a Sarrus linkage. The kinematic properties of these two components and of the combined unit are analyzed. The conditions under which the unit can be maximally compacted and deployed are determined through singularity analysis. New 2DOF DMs are obtained by linking the DUs: each mechanism's shape can be modified in two directions. The relationship between the degree of overconstraint and the number of DUs is derived. The magnification ratio is calculated as a function of link thickness and the number of DUs. The idea of deployment in independent directions is then extended to three dimensions with a family of 3DOF mechanisms. Finally, kinematic simulations are performed to validate the proposed designs and analyses.

Commentary by Dr. Valentin Fuster
J. Mechanisms Robotics. 2015;8(2):021009-021009-8. doi:10.1115/1.4031301.

Recent years show an increasing interest in flexible robots due to their adaptability merits. This paper introduces a novel set of hyper-redundant flexible robots which we call actuated flexible manifold (AFM). The AFM is a two-dimensional hyper-redundant grid surface embedded in $ℝ2$ or $ℝ3$. Theoretically, such a mechanism can be manipulated into any continuous smooth function. We introduce the mathematical framework for the kinematics of an AFM. We prove that for a nonsingular configuration, the number of degrees of freedom (DOF) of an AFM is simply the number of its grid segments. We also show that for a planar rectangular grid, every nonsingular configuration that is also energetically stable is isolated. We show how to calculate the forward and inverse kinematics for such a mechanism. Our analysis is also applicable for three-dimensional hyper-redundant structures as well. Finally, we demonstrate our solution on some actuated flexible grid-shaped surfaces.

Commentary by Dr. Valentin Fuster
J. Mechanisms Robotics. 2015;8(2):021010-021010-14. doi:10.1115/1.4031340.

A twisting problem is identified from the central located flexible backbone continuum robot. Regarding this problem, a design solution is required to mechanically minimize this twisting angle along the backbone. Further, the error caused by the kinematic assumption of previous works is identified as well, which requires a kinematic solution to minimize. The scope of this paper is to introduce, describe and teste a novel design of continuum robot which has a twin-pivot compliant joint construction that minimizes the twisting around its axis. A kinematics model is introduced which can be applied to a wide range of twin-pivot construction with two pairs of cables per section design. And according to this model, the approach for minimising the kinematic error is developed. Furthermore, based on the geometry and material property of compliant joint, the work volumes for single/three-section continuum robot are presented, respectively. The kinematic analysis has been verified by a three-section prototype of continuum robot and adequate accuracy and repeatability tests carried out. And in the test, the system generates relatively small twisting angles when a range of end loads is applied at the end of the arm. Utilising the concept presented in this paper, it is possible to develop a continuum robot which can minimize the twisting angle and be accurately controlled. In this paper, a novel design of continuum robot which has a twin-pivot compliant joint construction that minimizes the twisting around its axis is introduced, described and tested. A kinematics model is introduced which can be applied to a wide range of twin-pivot construction with two pairs of cables per section design. Furthermore, based on the geometry and material property of compliant joint, the work volumes for single/three-section continuum robot are presented, respectively. Finally, the kinematic analysis has been verified by a three-section prototype of continuum and adequate accuracy and repeatability tests carried out.

Topics: Kinematics , Robots , Cables , Design , Disks
Commentary by Dr. Valentin Fuster
J. Mechanisms Robotics. 2015;8(2):021011-021011-9. doi:10.1115/1.4031950.

Topics: Rotation , Linkages , Algebra
Commentary by Dr. Valentin Fuster
J. Mechanisms Robotics. 2015;8(2):021012-021012-8. doi:10.1115/1.4031302.

Below-knee amputation is one of the most frequently performed types of amputation in the United States. This paper describes CamWalk, a novel passive ankle prosthesis that has mechanical behavior similar to that of a natural ankle. CamWalk generates rotational push-off to propel the walker forward using a compliant coupling between two degrees-of-freedom (DOFs) (deflection along the leg and rotation about the ankle). The design closely matches the ankle torque and ankle work characteristics of an average healthy ankle. Simulation results indicate that CamWalk generates 44.5% of the net rotational work performed by a natural healthy ankle when leg deflection is limited to 15 mm. Standard gait analysis of four amputees using CamWalk demonstrated that the device performance ranged from marginally dissipative to significantly active, generating 48.0% of the work performed by their natural ankle.

Commentary by Dr. Valentin Fuster
J. Mechanisms Robotics. 2015;8(2):021013-021013-9. doi:10.1115/1.4031807.

Microrobotics is an ongoing study all over the world for which design is often inspired from macroscale robots. We have proposed the design of a new kind of microfabricated microrobot based on the use of binary actuators in order to generate a highly accurate and repeatable tool for positioning tasks at microscale without any sensor (with open-loop control). Our previous work consisted in the design, modeling, fabrication, and characterization of the first planar digital microrobot. In this paper, we focus on the motion planning of this robot for micromanipulation tasks. The complex motion pattern of this robot requires the use of algorithms. Graph theory is well suited for the discrete workspace generated by this robot. The comparison between several well-known trajectory-planning algorithms is done. A new graphical representation, named the hypercubic graph, is used for improving the computation speed of the algorithm. This is particularly useful for large workspace robots.

Commentary by Dr. Valentin Fuster
J. Mechanisms Robotics. 2015;8(2):021014-021014-9. doi:10.1115/1.4031657.

In this article, a novel method for characterizing the exact solution for interval linear systems is presented. In the proposed method, the entries of the interval coefficient matrix and interval right-hand side vector are formulated as linear functions of two or three parameters. The parameter groups for two- and three-parameter cases are identified. The exact solution is characterized using the solution sets corresponding to the parameter groups. The parametric method is then employed in the motion analysis of manipulators considering the uncertainty in kinematic parameters. Example manipulators are used to show the implementation of the method and the effect of uncertainty in the motion performance.

Commentary by Dr. Valentin Fuster
J. Mechanisms Robotics. 2015;8(2):021015-021015-13. doi:10.1115/1.4031679.

Understanding the geometry of gears with skew axes is a highly demanding task, which can be eased by invoking Study's Principle of Transference. By means of this principle, spherical geometry can be readily ported into its spatial counterpart using dual algebra. This paper is based on Martin Disteli's work and on the authors' previous results, where Camus' auxiliary curve is extended to the case of skew gears. We focus on the spatial analog of one particular case of cycloid bevel gears: When the auxiliary curve is specified as a pole tangent, we obtain “pathologic” spherical involute gears; the profiles are always interpenetrating at the meshing point because of G2-contact. The spatial analog of the pole tangent, a skew orthogonal helicoid, leads to G2-contact at a single point combined with an interpenetration of the flanks. However, when instead of a line a plane is attached to the right helicoid, the envelopes of this plane under the roll-sliding of the auxiliary surface (AS) along the axodes are developable ruled surfaces. These serve as conjugate tooth flanks with a permanent line contact. Our results show that these flanks are geometrically sound, which should lead to a generalization of octoidal bevel gears, or even of bevel gears carrying teeth designed with the exact spherical involute, to the spatial case, i.e., for gears with skew axes.

Commentary by Dr. Valentin Fuster
J. Mechanisms Robotics. 2015;8(2):021016-021016-9. doi:10.1115/1.4031951.

This paper presents the concept of variable radius drum mechanisms (VRDMs). A drum, or spool, consists of a spindle with flanges, around which a cable is wound. The cylindrical surface of an ordinary spool has a constant radius. In a variable radius drum (VRD), the radius of the spool varies along its profile. Properties of such devices are discussed, as well as the kinematic analysis and synthesis. The main contribution of the work is the theory of the VRD synthesis problem, rooted in a closed-form analytical solution. In order to highlight the benefits of VRDMs, two applications are presented and analyzed as examples. The first example consists of a mechanism which can support and guide a load along a horizontal linear path. The second example shows a solution to improve the locomotion of a legged robot. Finally, a prototype is made on the basis of the first case scenario and its performance is evaluated and discussed, showing a remarkable accuracy, with a deviation from the nominal trajectory of less than 1%.

Commentary by Dr. Valentin Fuster
J. Mechanisms Robotics. 2015;8(2):021017-021017-9. doi:10.1115/1.4031658.

This paper investigates the geometry of a foldable barrel vault with Yoshimura Origami patterns during the motion. On the base of the geometry analysis of the origami unit, the radius, span, rise, and longitudinal length of the foldable barrel vault with regular Yoshimura Origami pattern in all configurations throughout the motion are determined. The results show that the radius of curvature and the span increase during deployment. But the rise increases first, followed by a decrease with increasing fold angle. Furthermore, the influence of the apex angle of the origami unit and the numbers of triangular plates in the span direction on the geometric parameters is also investigated. Finally, the method to obtain the rise and span of the barrel vault with irregular origami pattern is also given.

Commentary by Dr. Valentin Fuster
J. Mechanisms Robotics. 2015;8(2):021018-021018-11. doi:10.1115/1.4031028.

Modeling large deflections has been one of the most fundamental problems in the research community of compliant mechanisms. Although many methods are available, there still exists a need for a method that is simple, accurate, and can be applied to a vast variety of large deflection problems. Based on the beam-constraint model (BCM), we propose a new method for modeling large deflections called chained BCM (CBCM), which divides a flexible beam into a few elements and models each element by BCM. The approaches for determining the strain energy stored in a deflected beam and the stress distributed on it are also presented within the framework of CBCM. Several typical examples were analyzed and the results show CBCMs capabilities of modeling various large deflections of flexible beams in compliant mechanisms. Generally, CBCM can serve as an efficient and versatile tool for solving large deflection problems in a variety of compliant mechanisms.

Commentary by Dr. Valentin Fuster
J. Mechanisms Robotics. 2015;8(2):021019-021019-10. doi:10.1115/1.4031168.

The purpose of this paper is to introduce a new kind of microarchitectured material that utilizes active control to alter its bulk shape through the deformation of its compliant elements. This new kind of microarchitectured material achieves its reconfigurable shape capabilities through a new control strategy that utilizes linearity and closed-form analytical tools to rapidly calculate the optimal internal actuation effort necessary to achieve a desired bulk surface profile. The kind of microarchitectured materials introduced in this paper is best suited for high-precision applications that would benefit from materials that can be programed to rapidly alter their surface or shape by small repeatable amounts in a controlled manner. Examples include distortion-correcting surfaces on which precision optics are mounted, airplane wings that deform to increase maneuverability and fuel efficiency, and surfaces that rapidly reconfigure to alter their texture. In this paper, the principles are provided for optimally designing 2D or 3D versions of the new kind of microarchitectured material such that they exhibit desired material property directionality. The mathematical theory is provided for modeling and calculating the actuation effort necessary to drive these materials such that their lattice shape comes closest to achieving a desired profile. Case studies are provided to demonstrate the utility of this theory and finite-element analysis (FEA) is used to verify the results.

Topics: Shapes , Actuators , Design , Stress
Commentary by Dr. Valentin Fuster
J. Mechanisms Robotics. 2015;8(2):021020-021020-10. doi:10.1115/1.4031952.

This paper presents a design approach to systematically synthesize feasible configurations for series–parallel and parallel hybrid transmissions subject to design constraints and required operation modes using a simple planetary gear train (PGT). The configuration synthesis process includes two main steps: (1) assign inputs and output powers to the PGT subject to design constraints by the power arrangement process and (2) assign clutches and brakes to the obtained systems subject to desired operation modes by the clutch arrangement process. By applying the proposed design approach, 9 clutchless and 31 clutched configurations for series–parallel and parallel hybrid transmission systems are synthesized, respectively. For each type of the hybrid systems, we analyzed kinematics and power flows of a new configuration to demonstrate the feasibility of the synthesized systems. The design approach can be used to systematically synthesize future hybrid transmissions with different mechanisms, design constraints, and desired operation modes.

Commentary by Dr. Valentin Fuster
J. Mechanisms Robotics. 2015;8(2):021021-021021-15. doi:10.1115/1.4031858.

The accuracy of a parallel kinematic mechanism (PKM) is directly related to its dynamic stiffness, which in turn is configuration dependent. For PKMs with kinematic redundancy, configurations with higher stiffness can be chosen during motion-trajectory planning for optimal performance. Herein, dynamic stiffness refers to the deformation of the mechanism structure, subject to dynamic loads of changing frequency. The stiffness-optimization problem has two computational constraints: (i) calculation of the dynamic stiffness of any considered PKM configuration, at a given task-space location, and (ii) searching for the PKM configuration with the highest stiffness at this location. Due to the lack of available analytical models, herein, the former subproblem is addressed via a novel effective emulator to provide a computationally efficient approximation of the high-dimensional dynamic-stiffness function suitable for optimization. The proposed method for emulator development identifies the mechanism's structural modes in order to breakdown the high-dimensional stiffness function into multiple functions of lower dimension. Despite their computational efficiency, however, emulators approximating high-dimensional functions are often difficult to develop and implement due to the large amount of data required to train the emulator. Reducing the dimensionality of the approximation function would, thus, result in a smaller training data set. In turn, the smaller training data set can be obtained accurately via finite-element analysis (FEA). Moving least-squares (MLS) approximation is proposed herein to compute the low-dimensional functions for stiffness approximation. Via extensive simulations, some of which are described herein, it is demonstrated that the proposed emulator can predict the dynamic stiffness of a PKM at any given configuration with high accuracy and low computational expense, making it quite suitable for most high-precision applications. For example, our results show that the proposed methodology can choose configurations along given trajectories within a few percentage points of the optimal ones.

Commentary by Dr. Valentin Fuster
J. Mechanisms Robotics. 2016;8(2):021022-021022-9. doi:10.1115/1.4032096.

This paper investigates the application of a planar deployable structure with screw theory and discusses its possible applications in overconstrained lift platforms via calculating its stiffness. These platforms are all made up of a number of identical scissor-form pivoted links. Compared with their traditional counterparts, the lift platforms with planar deployable structures have higher stiffness and higher strength in applications because every lift platform is multiplane overconstrained mechanism connected by a strengthened frame at each deployable layer. In operation, these deployable structures are always symmetric about the vertical central axis connecting the moving platform and the fixed one. Therefore, the stress conditions of the links in each layer can be assumed to be identical as the lift platform is moving up and down. Prototype test illustrates the innovation of the lift mechanisms while keeping the same load capacity.

Commentary by Dr. Valentin Fuster
J. Mechanisms Robotics. 2016;8(2):021023-021023-12. doi:10.1115/1.4032201.

A family of novel mechanisms with three limbs called sea lion ball mechanisms (SLBMs) is investigated that looks like a sea lion playing with a ball. The SLBM-type mechanism is composed of an upper part and a lower part connected together by three limbs in parallel, and the translational and rotational motions are fully/partially decoupled. The end-effector position is determined by inputs of the lower part, while the posture is mainly determined by inputs of the upper part. First, two compositional principles are abstracted and the corresponding mathematical models are built for the SLBM-type mechanisms that the commutative feature of the SLBMs is found. Then, two type synthesis procedures containing five steps are proposed correspondingly. Following the procedure, a family of novel four, five, and six degrees-of-freedom (DOF) SLBM-type mechanisms is synthesized systematically. The motion patterns of the limbs are enumerated according to the given desired ones of the mechanisms and the limbs are synthesized correspondingly. Finally, several novel SLBM-type mechanisms are achieved by assembling the obtained limbs and selecting the actuated joints.

Commentary by Dr. Valentin Fuster
J. Mechanisms Robotics. 2016;8(2):021024-021024-12. doi:10.1115/1.4032202.

This paper introduces a distributed variable impedance actuator that provides independent control of the actuator's angular position and its impedance. The idea for the actuator was inspired by the morphological structure of muscles and tendons. The system to be presented can be used as both a variable impedance actuator as well as a passive piecewise linear spring. Moreover, the actuator has an adequate number of degrees-of-freedom to approximate any nonlinear spring characteristics because of its distributed nature. Using distributed torque production subsystems with small and low power motors makes it possible to use this actuator in many applications such as prosthesis, artificial limbs, and wearable robots. The stability of the system discussed and the conditions that ensure the system stability are presented. Finally, a proof-of-concept actuator design is presented, as well as experimental results which confirm that the proposed distributed variable impedance actuator can be implemented in practical applications.

Commentary by Dr. Valentin Fuster
J. Mechanisms Robotics. 2016;8(2):021025-021025-9. doi:10.1115/1.4032101.

This paper presents a new design of a deployable one degree-of-freedom (DOF) mechanism. Polygonal rigid-link designs are first investigated. Then, belt-driven links are considered in order to maximize the expansion ratio while avoiding flattened ill-conditioned parallelogram configurations. The planar basic shape of the proposed design is a triangle. Hence, virtually any planar or spatial surface can be created by assembling such faces. For architecture and telescopic applications, the cupola assembly is investigated. The advantages of this approach are discussed, and the scalability is demonstrated. Finally, a prototype is built for illustration purposes.

Commentary by Dr. Valentin Fuster
J. Mechanisms Robotics. 2016;8(2):021026-021026-17. doi:10.1115/1.4028683.

Agriculture, forestry, and building industry would be prospective fields of robotic applications. High-rise tasks in these fields require robots with climbing skills. Motivated by these potential applications and inspired by animal climbing motion, we have developed a biped climbing robot—Climbot. Built with a modular approach, the robot consists of five joint modules connected in series and two special grippers mounted at the ends, with the scalability of changing degrees-of-freedom (DoFs). With this configuration, Climbot not only has superior mobility on multiple climbing media, such as poles and trusses, but also has the function of grasping and manipulating objects. It is a kind of “mobile” manipulator and represents an advancement in development of climbing robots. In this paper, we first present the development of this climbing robot with modular and bio-inspired methods, and then propose and compare three climbing gaits based on the unique configuration and features of the robot. A series of challenging and comprehensive experiments with the robot climbing in a truss and performing an outdoor manipulation task are carried out, to illustrate the feasibility, the features, the climbing, and manipulating functions of the robot, and to verify the effectiveness of the proposed gaits.

Commentary by Dr. Valentin Fuster
J. Mechanisms Robotics. 2016;8(2):021027-021027-10. doi:10.1115/1.4032403.

Two-degree-of-freedom (2DOF) pointing mechanisms have been widely used in areas such as stabilized platforms, tracking devices, etc. Besides the commonly used serial gimbal structures, another two types of parallel pointing mechanisms, i.e., spherical parallel manipulators (SPMs) and equal-diameter spherical pure rolling (ESPR) parallel manipulators, are increasingly concerned. Although all these pointing mechanisms have two rotational DOFs, they exhibit very different motion characteristics. A typical difference existing in these three pointing mechanisms can be found from their characteristics of self-motion, also called spinning motion by the authors. In this paper, the spinning motions of three pointing mechanisms are modeled and compared via the graphical approach combined with the vector composition theorem. According to our study, the spinning motion is essentially one component of the moving platform's real rotation. Furthermore, image distortions caused by three spinning motions are identified and distinguished when the pointing mechanisms are used as tracking devices. Conclusions would facilitate the design and control of the pointing devices and potentially improve the measuring accuracy for targets pointing and tracking.

Commentary by Dr. Valentin Fuster
J. Mechanisms Robotics. 2016;8(2):021028-021028-8. doi:10.1115/1.4032588.

From a perspective of robot kinematics, we develop a method for predicting internal motion properties and understanding the functions of proteins from their three-dimensional (3D) structural data (protein data bank (PDB) data). The key ideas are based on the structural compliance analysis of proteins. In this paper, we mainly discuss the basic equations for the analysis. First, a kinematic model of a protein is introduced. Proteins are simply modeled as serial manipulators constrained by linear springs, where the dihedral angles on the main chains correspond to the joint angles of manipulators. Then, the kinematic equations of the protein model are derived. In particular, the forced response or the deformation caused by the forces in static equilibrium forms the basis for the structural compliance analysis. In the formulations, the protein models are regarded as manipulators that control the positions in the model or the distances between them, by the dihedral angles on the main chains. Next, the structural compliance of the protein model is defined, and a method for extracting the information about the internal motion properties from the structural compliance is shown. In general, the structural compliance refers to the relationship between the applied forces and the deformation of the parts surrounded by the application points. We define it in a more general form by separating the parts whose deformations are evaluated from those where forces are applied. When decomposing motion according to the magnitude of the structural compliance, we can infer that the lower compliance motion will easily occur. Finally, we show two application examples using PDB data of lactoferrin and hemoglobin. Despite using an approximate protein model, the predicted internal motion properties agree with the measured ones.

Commentary by Dr. Valentin Fuster
J. Mechanisms Robotics. 2016;8(2):021029-021029-18. doi:10.1115/1.4032097.

The method of intersection of surfaces generated by kinematic dyads is applied to obtain mechanisms that are able to shift from one mode of motion to another. Then a mobility analysis shows that the singularities of the generated surfaces can be used to obtain mechanisms which can change their number of degrees-of-freedom depending on its configuration. The generator dyads are connected as usually done by a spherical pair. However, in the cases shown in this contribution the three-degrees-of-freedom of the spherical pair are not all necessary to keep the kinematic chain closed and movable, and the spherical pair can be substituted by either a pair of intersecting revolute joints or a single revolute joint. This substitution can be obtained by means of two methods presented in this contribution.

Commentary by Dr. Valentin Fuster

### Technical Brief

J. Mechanisms Robotics. 2015;8(2):024501-024501-3. doi:10.1115/1.4031656.

The determination of workspace is an essential step in the development of parallel manipulators. By extending the virtual-chain (VC) approach to the type synthesis of parallel manipulators, this technical brief proposes a VC approach to the workspace analysis of parallel manipulators. This method is first outlined before being illustrated by the production of a three-dimensional (3D) computer-aided-design (CAD) model of a 3-RPS parallel manipulator and evaluating it for the workspace of the manipulator. Here, R, P and S denote revolute, prismatic and spherical joints respectively. The VC represents the motion capability of moving platform of a manipulator and is shown to be very useful in the production of a graphical representation of the workspace. Using this approach, the link interferences and certain transmission indices can be easily taken into consideration in determining the workspace of a parallel manipulator.

Commentary by Dr. Valentin Fuster