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### Guest Editorial

J. Mechanisms Robotics. 2019;11(2):020301-020301-1. doi:10.1115/1.4042958.
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For 42 years, the Mechanisms and Robotics (M&R) Conference has provided an international venue for presentation and discussion of the latest scientific and technical results in the broad field of mechanical systems and their applications. This includes the design (novel mechanisms and robots, synthesis), analysis (kinematics, dynamics, computational approaches, and software systems), applications (from micro-air vehicles, modular robotics, origami applications, medical robotics, to exoskeleton-assistive systems), and educational practices. This fifth IDETC Special Issue contains selected papers from active researchers that have presented results of archival value. The reader will appreciate the wide span of topics showcasing the diversity and quality of the symposia that were organized within the M&R conference.

Commentary by Dr. Valentin Fuster

### Special Section: Selected Papers from IDETC 2018

J. Mechanisms Robotics. 2019;11(2):020901-020901-8. doi:10.1115/1.4042485.

This paper extends the use of velocity decomposition of underactuated mechanical systems to the design of an enhanced hybrid zero dynamics (HZD)-based controller for biped robots. To reject velocity disturbances in the unactuated degree-of-freedom, a velocity decomposition-enhanced controller implements torso and leg offsets that are proportional to the error in the time derivative of the unactuated velocity. The offsets are layered on top of an HZD-based controller to preserve simplicity of implementation. Simulation results with a point-foot, three-link planar biped show that the proposed method has nearly identical performance to transverse linearization feedback control and outperforms conventional HZD-based control. Curved feet are implemented in simulation and show that the proposed control method is valid for both point-foot and curved-foot planar bipeds. Performance of each controller is assessed by (1) the magnitude of the disturbance it can reject by numerically computing the basin of attraction, (2) the speed of return to nominal step velocity following a disturbance at every point of the gait cycle, and (3) the energetic efficiency, which is measured via the specific cost of transport. Several gaits are analyzed to demonstrate that the observed trends are consistent across different walking speeds.

Commentary by Dr. Valentin Fuster
J. Mechanisms Robotics. 2019;11(2):020902-020902-9. doi:10.1115/1.4042457.

This paper presents the design, modeling, and analysis of the force behavior acting on a wheel-legs (whegs) type robot which utilizes bilayer dry adhesives for wall-climbing. The motion of the robot is modeled as a slider-crank mechanism to obtain the dynamic parameters of the robot during movement. The required forces and moment to maintain equilibrium as the robot is in motion is then extensively analyzed and discussed. Following the analysis, fundamental measures to attain an operative climbing robot, such as adhesive requirement and torque specification, are then identified. The outcomes of the analysis are verified through experiments and working prototypes that are in good agreement with the design guidelines.

Commentary by Dr. Valentin Fuster
J. Mechanisms Robotics. 2019;11(2):020903-020903-10. doi:10.1115/1.4042486.

This paper presents a trajectory planning approach and an analysis of the geometric design parameters for a planar cable-suspended translational parallel robot based on a parallelogram cable loop. The cable robot produces purely translational movements in a planar workspace. Furthermore, this special architecture only requires two actuators, which make it fully actuated. From the dynamic model of the robot, general algebraic inequalities are obtained that ensure that the cables remain taut. A general elliptic trajectory is then defined and substituted into the algebraic inequalities to obtain conditions on the geometrical design parameters that ensure that the cables are always in tension. In addition, a special trajectory-specific oscillation frequency emerges and enables the end effector to dynamically move beyond the boundaries of the static workspace, thus expanding the workspace of the mechanism. Finally, a kinematic sensitivity index is studied in order to determine if the parallelogram structure has any influence on the rotational sensitivity of the mechanism.

Commentary by Dr. Valentin Fuster
J. Mechanisms Robotics. 2019;11(2):020904-020904-9. doi:10.1115/1.4042427.

This work introduces a type of motion termed “conceal-and-reveal” which is characterized by a state that protects a payload, a state that exposes the payload, and coupled motions between these two states. As techniques for thick, rigid origami-based engineering designs are being developed, origami is becoming increasingly more attractive as inspiration for complex systems. This paper proposes a process for designing origami-based conceal-and-reveal systems, which can be generalized to design similar thick, rigid origami-based systems. The process is demonstrated through the development of three conceal-and-reveal systems that present a luxury product to the consumer. The three designs also confirm that multiple origami crease patterns can be used to initiate viable approaches to achieving conceal-and-reveal motion.

Topics: Design , Manufacturing
Commentary by Dr. Valentin Fuster
J. Mechanisms Robotics. 2019;11(2):020905-020905-10. doi:10.1115/1.4042512.

Traditional topology optimization techniques, such as density-based and level set methods, have proven successful in identifying potential design configurations for structures and mechanisms but suffer from rapidly increasing design space dimensionality and the possibility of converging to local minima. A heuristic alternative to these approaches couples a genetic algorithm with a Lindenmayer system (L-system), which encodes design variables and governs the development of the structure when coupled with an interpreter to translate genomic information into structural topologies. This work discusses the development of a graph-based interpretation scheme referred to as spatial interpretation for the development of reconfigurable structures (SPIDRS). This framework allows for the effective exploration of mechanism design spaces using a limited number of design variables. The theory and implementation of this method are detailed, and multiple case studies are presented to demonstrate the ability of SPIDRS to generate adaptive structures capable of achieving multiple design goals.

Commentary by Dr. Valentin Fuster
J. Mechanisms Robotics. 2019;11(2):020906-020906-8. doi:10.1115/1.4042475.

Many kinematic problems in mechanisms can be represented by polynomial systems. By algebraically analyzing the polynomial systems, we can obtain the kinematic properties of the mechanisms. Among these algebraic methods, approaches based on Gröbner bases are effective. Usually, the analyses are performed for specific mechanisms; however, we often encounter phenomena for which, even within the same class of mechanisms, the kinematic properties differ significantly. In this research, we consider the cases where the parameters are included in the polynomial systems. The parameters are used to express link lengths, displacements of active joints, hand positions, and so on. By analyzing a parametric polynomial system (PPS), we intend to comprehensively analyze the kinematic properties of mechanisms represented by these parameters. In the proposed method, we first express the kinematic constraints in the form of PPS. Subsequently, by calculating the Gröbner cover of the PPS, we obtain the segmentation of the parameter space and valid Gröbner bases for each segment. Finally, we interpret the meaning of the segments and their corresponding Gröbner bases. We analyzed planar four- and five-bar linkages and five-bar truss structures using the proposed method. We confirmed that it was possible to enumerate the assembly and working modes and to identify the geometrical conditions that enable overconstrained motions.

Commentary by Dr. Valentin Fuster
J. Mechanisms Robotics. 2019;11(2):020907-020907-8. doi:10.1115/1.4042458.

A novel construction method is proposed to construct multimode deployable polyhedron mechanisms (DPMs) using symmetric spatial RRR compositional units, a serial kinematic chain in which the axes of the first and the third revolute (R) joints are perpendicular to the axis of the second R joint. Single-loop deployable linkages are first constructed using RRR units and are then assembled into polyhedron mechanisms by connecting the single-loop linkages using RRR units. The proposed mechanisms are over-constrained and can be deployed. The prism mechanism constructed using two Bricard linkages and six RRR chains has one degree-of-freedom (DOF). When removing three of the RRR chains, the mechanism will have one additional 1-DOF motion mode. The DPMs based on 8R and 10R linkages also have multiple modes, and several mechanisms have variable-DOF. The DPMs can switch among different motion modes through transition positions. Prototypes are 3D-printed to verify the feasibility of the mechanisms.

Commentary by Dr. Valentin Fuster
J. Mechanisms Robotics. 2019;11(2):020908-020908-8. doi:10.1115/1.4042476.

This paper explores the ability to tailor the mechanical properties of composite compliant shell mechanisms, by exploiting the thermal prestress introduced during the composite laminate cure. An extension of an analytical tape spring model with composite thermal analysis is presented, and the effect of the thermal prestress is studied by means of energy landscapes for the cylindrical composite shells. Tape springs that would otherwise be monostable structures become bistable and exhibit greater ranges of low-energy twisting with thermally induced prestress. Predicted shell geometries are compared with finite element (FE) results and manufactured samples, showing good agreement between all approaches. Wider challenges around the manufacture of prestressed composite compliant mechanisms are discussed.

Commentary by Dr. Valentin Fuster
J. Mechanisms Robotics. 2019;11(2):020909-020909-12. doi:10.1115/1.4042513.

Aerial cable towed systems (ACTSs) can be created by joining unmanned aerial vehicles (UAVs) to a payload to extend the capabilities of the system beyond those of an individual UAV. This paper describes a systematic method for evaluating the available wrench set and the robustness of equilibrium of ACTSs by adapting wrench analysis techniques used in traditional cable-driven parallel robots to account for the constraints of quadrotor actuation and dynamics. Case studies and experimental results are provided to demonstrate the analysis of different classes of ACTSs, as a means of evaluating the design and operating configurations.

Topics: Cables , Tension , Thrust
Commentary by Dr. Valentin Fuster
J. Mechanisms Robotics. 2019;11(2):020910-020910-9. doi:10.1115/1.4042545.

A motion of a mechanism is a curve in its configuration space (c-space). Singularities of the c-space are kinematic singularities of the mechanism. Any mobility analysis of a particular mechanism amounts to investigating the c-space geometry at a given configuration. A higher-order analysis is necessary to determine the finite mobility. To this end, past research leads to approaches using higher-order time derivatives of loop closure constraints assuming (implicitly) that all possible motions are smooth. This continuity assumption limits the generality of these methods. In this paper, an approach to the higher-order local mobility analysis of lower pair multiloop linkages is presented. This is based on a higher-order Taylor series expansion of the geometric constraint mapping, for which a recursive algebraic expression in terms of joint screws is presented. An exhaustive local analysis includes analysis of the set of constraint singularities (configurations where the constraint Jacobian has certain corank). A local approximation of the set of configurations with certain rank is presented, along with an explicit expression for the differentials of Jacobian minors in terms of instantaneous joint screws. The c-space and the set of points of certain corank are therewith locally approximated by an algebraic variety determined algebraically from the mechanism's screw system. The results are shown for a simple planar 4-bar linkage, which exhibits a bifurcation singularity and for a planar three-loop linkage exhibiting a cusp in c-space. The latter cannot be treated by the higher-order local analysis methods proposed in the literature.

Commentary by Dr. Valentin Fuster
J. Mechanisms Robotics. 2019;11(2):020911-020911-9. doi:10.1115/1.4042544.

This paper describes the design and control architecture of a novel wheelchair-mounted robot for active postural support (WRAPS). The WRAPS is a robotic exoskeleton that allows limited degrees-of-freedom of the trunk relative to the pelvis. There are three degrees-of-freedoms in the sagittal plane of the human body and one in lateral bending. The work is motivated by the needs of individuals with impaired trunk motor control, who currently rely on the use of passive and predominantly static supports to maintain a static posture. These devices can be overly restrictive and inhibit the user in their activities of daily living. The WRAPS is capable of supporting a human user within their active range of torso motion. It has the potential to assist users in their activities of daily living while encouraging a dynamic range of healthy postures.

Commentary by Dr. Valentin Fuster
J. Mechanisms Robotics. 2019;11(2):020912-020912-7. doi:10.1115/1.4042641.

Tape springs are thin-walled structures with zero longitudinal and constant transverse curvature. Folding them twice and connecting both ends creates a tape loop which acts as a linear guide. At this time, there is insufficient understanding of the influence of the tape spring's cross section on its behavior. This study investigates the influence of the subtended angle on the tape spring's behavior, especially the energy distribution and the fold radius. First, some key aspects in the design of a twofold tape loop are discussed. By performing a curvature analysis of this folded geometry, the different regions within a tape spring are identified. This information is used to identify the influence of the subtended angle on the geometry and energy state of the tape loop. The fold radius and fold angle are determined by analyzing the geometry of the fold region. The analysis showed that the energy within the transition regions cannot be neglected. The energy within these regions and the length of the transition regions both increase with the subtended angle. It is also shown that the fold radius is not constant when the subtended angle is small. The subtended angle should be above 100 deg to ensure a constant radius.

Topics: Springs , Geometry
Commentary by Dr. Valentin Fuster
J. Mechanisms Robotics. 2019;11(2):020913-020913-10. doi:10.1115/1.4042514.

The extended Jacobian is a technique for solving the redundancy of redundant robots. It is based on the definition of secondary tasks, through constraint functions that are added to the mapping between joint rates and end-effector's twist. Several approaches showed its potential, applications, and limitations. In general, the constraint functions are a linear combination of basic functions with constant coefficients. This paper proposes the use of adaptive coefficients in such functions by using the conditioning index of the extended Jacobian as a quality measure. A good conditioning index of the extended Jacobian keeps the robot far from singularities and contributes to the solution of the inverse kinematics. In this paper, initially, the extended Jacobian and the proposed algorithm are discussed, and then, two tests in different circumstances are presented in order to validate the proposal.

Commentary by Dr. Valentin Fuster
J. Mechanisms Robotics. 2019;11(2):020914-020914-9. doi:10.1115/1.4042543.

In this paper, the design of compliant three-dimensional (3D) printed surgical end-effectors for robotic lumbar discectomy is presented. Discectomy is the surgery to remove the herniated disk material that is pressing on a nerve root or spinal cord. This surgery is performed to relieve pain or numbness caused by the pressure on the nerve. The limited workspace of the spine (<27 cm3) results in challenging design requirements for surgical instruments. We propose a new cannula-based robotic lumbar discectomy procedure that can accommodate multiple articulated tools in the workspace at the same time and can be controlled teleoperatively by the surgeon. We present designs for two instruments for this proposed system: an articulated nerve retractor and an articulated grasper. The end-effectors of each are 3D printed with multiple materials, with flexible links acting as joints of the mechanism. These flexible links are actuated by cables which provide sufficient articulation and manipulation forces in the surgical workspace. The end-effector's articulated flexible joint kinematics is modeled and tested for range of motion capabilities. The retraction forces for the nerve retractor and the grasping force for the grasper are also experimentally tested and verified to meet all the design requirements. Additionally, fatigue testing of the flexible joint is presented and teleoperated control for the instruments is demonstrated. Finally, conceptual designs for new actuation systems are presented that will enable feasible surgical operations with the enhanced attributes of the designed end-effectors.

Commentary by Dr. Valentin Fuster
J. Mechanisms Robotics. 2019;11(2):020915-020915-7. doi:10.1115/1.4042295.

This paper presents the design of a two-degrees-of-freedom (DoFs) variable stiffness mechanism and demonstrates how its adjustable compliance can enhance the robustness of physical human–robot interaction. Compliance on the grasp handle is achieved by suspending it in between magnets in preloaded repelling configuration to act as nonlinear springs. By adjusting the air gaps between the outer magnets, the stiffness of the mechanism in each direction can be adjusted independently. Moreover, the capability of the proposed design in suppressing unintended interaction forces is evaluated in two different experiments. In the first experiment, improper admittance controller gain leads to unstable interaction, whereas in the second case, high-frequency involuntary forces are caused by the tremor.

Commentary by Dr. Valentin Fuster

### Research Papers

J. Mechanisms Robotics. 2019;11(2):021001-021001-10. doi:10.1115/1.4041942.

The use of cable-driven parallel robots (CDPR) in real-world applications makes safety a major concern for these devices and a relevant research topic. Cable-suspended camera systems are among the earliest and most common applications of CDPRs. In this paper, we propose a novel after-failure approach for cable-suspended camera systems. This strategy, which is applied after a cable breaks, seeks to drive the end effector, i.e., the camera, toward a safe pose, following an oscillatory trajectory that guarantees positive and bounded tensions in the remaining cables. The safe landing location is optimized to minimize the trajectory time while avoiding collisions with the physical boundaries of the workspace. Results of numerical simulations indicate the feasibility of the proposed approach.

Commentary by Dr. Valentin Fuster
J. Mechanisms Robotics. 2019;11(2):021002-021002-8. doi:10.1115/1.4042348.

A novel parallel kinematics machine (PKM) stemming from the 3-SRU (spherical-revolute-universal) under-actuated joints topology is presented in this paper. The concept here proposed takes advantage of a reconfigurable universal joint obtained by locking, one at a time, different rotations of a spherical pair. Such local reconfiguration causes a slight, yet crucial, modification of the robot legs mobility which is enough to provide the end-effector with different kinds of motion. In particular, the kinematic chain is converted to two different 3-URU architectures (universal-spherical-universal) able to provide the moving platform with essentially different mobilities. The paper is dedicated at formally demonstrating the motion capabilities offered by such parallel architectures. To this aim, the first part of the paper describes the mechanical structures and formalizes the kinematic problem through appropriate sets of polynomial equations. Then, an analysis of the equations is proposed to uniquely identify the mobilities of the moving platform. At last, a concept design is proposed for the reconfigurable spherical platform.

Commentary by Dr. Valentin Fuster
J. Mechanisms Robotics. 2019;11(2):021003-021003-12. doi:10.1115/1.4042347.

This paper describes the use of an active disturbance rejection controller (ADRC) to estimate and compensate for the effect of slip in an online manner to improve the path tracking performance of autonomous ground vehicles (AGVs). AGVs with skid-steer locomotion mode are extensively used for robotic applications in the fields of agriculture, transportation, construction, warehouse maintenance, and mining. Majority of these applications such as performing reconnaissance and rescue operations in rough terrain or autonomous package delivery in urban scenarios, require the system to follow a path predetermined by a high-level planner or based on a predefined task. In the absence of effective slip estimation and compensation, the AGVs, especially tracked vehicles, can fail to follow the path as given out by the high-level planner. The proposed ADRC architecture uses a generic mathematical model that can account for the scaling and shift in the states of the system due to the effects of slip through augmented parameters. An extended Kalman filter (EKF) observer is used to estimate the varying slip parameters online. The estimated parameters are then used to compensate for the effects of slip at each iteration by modifying the control actions given by a low-level path tracking controller. The proposed approach is validated through experiments over flat and uneven terrain conditions including asphalt, vinyl flooring, artificial turf, grass, and gravel using a tracked skid-steer mobile robot. A detailed discussion on the results and directions for future research is also presented.

Commentary by Dr. Valentin Fuster
J. Mechanisms Robotics. 2019;11(2):021004-021004-10. doi:10.1115/1.4042349.

Soft linear actuators (SLAs) make linear displacement by shrinkage and relaxation like skeletal muscles, so they can be called as artificial skeletal muscles (ASMs). They deform their body to create displacement. However, the restoring force generated by the deformation of their soft body reduces the force available from the SLA. This actuation structure is a critical drawback in the application of SLAs. In a living body, skeletal muscle is the main actuator to make movement. In order to make meaningful movements, skeletal muscles of a living body require bones and joints. Thus, as well as ASMs, artificial joints are surely required for developing robotic applications such as robotic prosthetics and bionic body parts. This paper introduces a biomimetic artificial joint mechanism that can improve the drawback of SLA. The basic performance and usefulness of the joint mechanism was confirmed by using shape-memory-alloy actuators (called SMA in general). In addition, the joint control strategy of the joint mechanism by adopting the joint control principle of a living body was proposed and its performance was experimentally validated.

Commentary by Dr. Valentin Fuster
J. Mechanisms Robotics. 2019;11(2):021005-021005-10. doi:10.1115/1.4042346.

This paper presents methods to exploit the redundancy of a kinematically redundant spatial parallel mechanism with three redundant DOFs. The architecture of the mechanism is similar to the well-known Gough–Stewart (GS) platform and it retains its advantages, i.e., the members connecting the base to the moving platform are only subjected to tensile/compressive loads. The kinematic redundancy is exploited to avoid singularities and extend the rotational workspace. The architecture is described and the associated kinematic relationships are presented. Solutions for the inverse kinematics are given, as well as strategies to take into account the limitations of the mechanism such as mechanical interferences and velocity limits of the actuators while controlling the redundant degrees-of-freedom.

Commentary by Dr. Valentin Fuster
J. Mechanisms Robotics. 2019;11(2):021006-021006-9. doi:10.1115/1.4041889.

The parameterization of rotations is a central topic in many theoretical and applied fields such as rigid body mechanics, multibody dynamics, robotics, spacecraft attitude dynamics, navigation, three-dimensional image processing, and computer graphics. Nowadays, the main alternative to the use of rotation matrices, to represent rotations in $ℝ3$, is the use of Euler parameters arranged in quaternion form. Whereas the passage from a set of Euler parameters to the corresponding rotation matrix is unique and straightforward, the passage from a rotation matrix to its corresponding Euler parameters has been revealed to be somewhat tricky if numerical aspects are considered. Since the map from quaternions to 3 × 3 rotation matrices is a 2-to-1 covering map, this map cannot be smoothly inverted. As a consequence, it is erroneously assumed that all inversions should necessarily contain singularities that arise in the form of quotients where the divisor can be arbitrarily small. This misconception is herein clarified. This paper reviews the most representative methods available in the literature, including a comparative analysis of their computational costs and error performances. The presented analysis leads to the conclusion that Cayley's factorization, a little-known method used to compute the double quaternion representation of rotations in four dimensions from 4 × 4 rotation matrices, is the most robust method when particularized to three dimensions.

Commentary by Dr. Valentin Fuster

### Technical Brief

J. Mechanisms Robotics. 2019;11(2):024501-024501-4. doi:10.1115/1.4042296.

Spherical robots have a wide range of self-propulsion mechanisms. Of particular interest in this paper are propulsion systems where wheels are placed in contact with the inner surface of the spherical shell of the robot. Here, locomotion is achieved by a combination of the actions of the motors along with the rolling constraints at the point of contact of the shell with the ground surface. We ask and seek the answer to the following question using elementary arguments: What is the minimal number of actuations needed to completely prescribe the motion of the robot for the two distinct cases where it is rolling and sliding on a surface? We find that two points of actuation are all that is needed provided some simple geometric conditions are satisfied. Our analysis is then applied to the BB-8 robot to show how locomotion is achieved in this robot.

Commentary by Dr. Valentin Fuster
J. Mechanisms Robotics. 2019;11(2):024502-024502-7. doi:10.1115/1.4042345.

This paper shows an experimental validation for the design of a three-degree-of-freedom (DOF) cable-suspended parallel robot, which has six cables attached to the end-effector, arranged in three pairs, with each pair being driven by a single motor. For each pair, the moving platform attachment points and the winch cable guides on the fixed frame form a parallelogram, an arrangement that allows the end-effector to be positioned throughout its static workspace (SW) while maintaining a constant orientation. In this paper, the kinematic modeling of the robot is first described, along with its SW. Then, the robot's kinematic sensitivity is assessed in position and orientation such that an upper bound is found for the amplification of the cable positioning errors in Cartesian space. Finally, experimental results obtained using a proof-of-concept mechanism are described, which confirm the claim that the proposed design maintains a constant platform orientation in the SW.

Commentary by Dr. Valentin Fuster