We present a novel, rigidly folding vertex inspired by the shape of the simplest hanging drape. Fold lines in the vertex correspond to pleats and ridges in the drape and are symmetrically arranged to enable synchronized flat folding of facet pairs. We calculate the folded rotation angles exactly using a spherical image specialized for inextensible vertex folding. We show that the vertex shape is bounded by a pair of conical surfaces whose apex semi-angles directly correspond with fold-line rotations, which expresses a geometrical equivalence between the external shape and internal folding motion of the vertex. We discuss how the vertex, viz. drape, perform as a novel type of conical defect based on its spherical image topography, and we highlight the meaning of bistable behavior for the vertex in analytical and practical terms.

Soft robotic grippers can gently grasp and maneuver objects. However, they are difficult to model and control due to their highly deformable fingers and complex integration with robotic systems. This paper investigates the design requirements as well as the grasping capabilities and performance of a soft gripper system based on fluidic prestressed composite (FPC) fingers. An analytical model is constructed as follows: each finger is modeled using the chained composite model (CCM); strain energy and work done by pressure and loads are computed using polynomials with unknown coefficients; net energy is minimized using the Rayleigh–Ritz method to calculate the deflected equilibrium shapes of the finger as a function of pressure and loads; and coordinate transformation and gripper geometries are combined to analyze the grasping performance. The effects of prestrain, integration angle, and finger overlap on the grasping performance are examined through a parametric study. We also analyze gripping performance for cuboidal and spherical objects and show how the grasping force can be controlled by varying fluidic pressure. The quasi-static responses of fabricated actuators are measured under pressures and loads. It is shown that the actuators’ modeled responses agree with the experimental results. This work provides a framework for the theoretical analysis of soft robotic grippers and the methods presented can be extended to model grippers with different types of actuation.

The paper deals with the elastostatic modeling of a multi-link flexible manipulator based on the two-dimensional (2D) dual-triangle tensegrity mechanism and its nonlinear behavior under external loading. The main attention is paid to the static equilibriums and the manipulator stiffness behavior under the loading for the arbitrary initial configuration. It was proved that there is a quasi-buckling phenomenon for this manipulator while the external loading is increasing. In the neighborhood of these configurations, the manipulator behavior was analyzed using the enhanced virtual joint method (VJM). A relevant simulation study confirmed the obtained theoretical results.

The jamming mechanism is a crucial method to tune the stiffness of soft-bodied machines to adapt to their surroundings. However, it is difficult for the present jamming structures to integrate them into systems with complicated shapes such as twist, cylinder, and spiral. This paper introduces a novel jamming mechanism termed a filament jamming technique, which varies stiffness using jamming of a cluster of tiny and compliant filaments. The jamming structure demonstrated various characteristics such as softness, shape compatibility, lightweight, and high stiffness. These feats can meet a variety of application scenarios that the traditional jamming one cannot afford. The experimental test was used to explore the jamming structure's stiffness behavior and dynamic performance. The influence of the filament structure dimensions, material properties, and the vacuum pressure on the stiffness was revealed. With the negative pressure increasing, both the natural frequency and damping ratio increase due to the rigidity variation. It indicates that the filament jamming structure has excellent response rapidity and shock resistance. Our work demonstrated some versatile features of the filament jamming technology, like shape adaptation, shape-preserving, stiffness stability, and compliance. To demonstrate the advantage of the jamming technique, we constructed a soft gripper and a torsional actuator to illustrate how the mechanics of filament jamming can enhance real-world robotics systems’ performance. Therefore, the filament jamming mechanism provides various machines and structures with additional properties to increase forces transmitted to the environment and tune response and damping. This study aims to foster a new generation of mechanically versatile machines and structures with softness and stiffness.

The design of robots at the small scale is a trial-and-error based process, which is costly and time-consuming. There are few dynamic simulation tools available to accurately predict the motion or performance of untethered microrobots as they move over a substrate. At smaller length scales, the influence of adhesion and friction, which scales with surface area, becomes more pronounced. Thus, rigid body dynamic simulators, which implicitly assume that contact between two bodies can be modeled as point contact, are not suitable. In this paper, we present techniques for simulating the motion of microrobots where there can be intermittent and non-point contact between the robot and the substrate. We use these techniques to study the motion of tumbling microrobots of different shapes and select shapes that are optimal for improving locomotion performance. Simulation results are verified using experimental data on linear velocity, maximum climbable incline angle, and microrobot trajectory. Microrobots with improved geometry were fabricated, but limitations in the fabrication process resulted in unexpected manufacturing errors and material/size scale adjustments. The developed simulation model can incorporate these limitations and emulate their effect on the microrobot’s motion, reproducing the experimental behavior of the tumbling microrobots, further showcasing the effectiveness of having such a dynamic model.

In this article, we present a continuously tunable stiffness arm for safe physical human–robot interactions. Compliant joints and compliant links are two typical solutions to address safety issues for physical human–robot interactions via introducing mechanical compliance to robotic systems. While extensive studies explore variable stiffness joints/actuators, variable stiffness links for safe physical human–robot interactions are much less studied. This article details the design and modeling of a compliant robotic arm whose stiffness can be continuously tuned via cable-driven mechanisms actuated by a single servo motor. Specifically, a 3D-printed compliant robotic arm is prototyped and tested by static experiments, and an analytical model of the variable stiffness arm is derived and validated by testing. The results show that the lateral stiffness of the robot arm can achieve a variety of 221.26% given a morphing angle of 90 deg. The variable stiffness arm design developed in this study could be a promising approach to address safety concerns for safe physical human–robot interactions.

This article reports a method for regulating the internal forces during in-hand manipulation of an unknown shaped object with soft robotic fingers. The internal forces ensure that the object does not move between the robotic fingers, thus improving the grip. It is shown that if soft fingers show bounded conformity and the finger–object interface have bounded relative slip, then the relative angular velocity between the object and the fingertip coordinate frame in contact is bounded. Detailed derivation of the proof is presented. The proof is later used to define a new metric of relative slip. The metric is used to design a sliding mode control algorithm that results in an efficient grip, which is robust toward uncertainty in object shape. The robotic fingers are assumed to be under virtual rigidity constraint, that is, the distance between the fingertips do not change. The control algorithm is attractive as it skirts requirement of information of the shape of the object or to solve optimization problems. The grip with the robust control algorithm is shown to be finite-time stable through Lyapunov’s method. The methodology is demonstrated using simulations.

The ability to deploy a planar surface to a desired convex profile with a simple actuation can enhance foldable or morphing airfoils, deployable antennae and reflectors, and other applications where a specific profile geometry is desired from a planar sheet. A model using a system of rigid links joined by torsional springs of tailorable stiffness is employed to create an approximate curved surface when two opposing tip loads are applied. A system of equations describing the shape of the surface during deployment is developed. The physical implementation of the model uses compliant torsion bars as the torsion springs. A multidimensional optimization algorithm is presented to place joints to minimize the error from the rigid-link approximation and account for additional manufacturing and stress considerations in the torsion bars. A proof is presented to show that equal torsion spring spacing along the horizontal axis of deployed parabolic profiles will result in minimizing the area between the model’s rigid-link approximation and smooth curve. The model is demonstrated through the physical construction of a deployable airfoil surface and a metallic deployable parabolic reflector.

In this paper, a complete morphing system consisting of a variable geometry truss manipulator (VGTM) is presented that is fully covered by a flexible panel skin. Two approaches are studied for the morphing control. The first one is to have the VGTM act as a driving mechanism and the flexible panels as a passive system. In this case, the VGTM is composed of active members and passive lockable members. It is shown that the morphing system can reach the desired shapes through intermediate steps. The second method is to have the flexible panels act as drivers and the VGTM as a passive supporting structure. In this case, the VGTM is only composed of passive lockable members. The morphing system can also achieve the desired poses through several steps. The control strategies of the two methods are discussed along with kinematic analysis, a comparison study is conducted to show their pros and cons, two prototypes are fabricated, and experiments are carried out to verify the feasibility of two actuation methods.

Over the past few years, the concept of multi-directional three-dimensional (3D) printing has been introduced to print complex shapes and overhang geometry. This technique requires the nozzle to constantly change orientation to print the object along its tangential direction. A six-degrees-of-freedom (6-DOF) robotic arm or Stewart platform can be a solution, but these mechanisms use more components and motors. An alternative solution has been proposed in this paper based on a four-CRU (cylindrical, revolute, and universal joints) mechanism. This mechanism can orient the nozzle by switching into different motion types with minimal numbers of motors while keeping the mechanism rigid and agile. Therefore, analyses of the reconfiguration, workspace, singularities, and self-motions of a four-CRU mechanism presented in this paper have become necessities. By using primary decomposition, four geometric constraints have been identified, and the reconfiguration analysis has been carried out in each of these. It reveals that each geometric constraint will have three distinct operation modes, namely Schönflies mode, reversed Schönflies mode, and an additional mode. The additional mode can either be a four-DOF mode or a degenerated three-DOF mode, depending on the type of geometric constraints. By taking into account the actuation and constraint singularities, the workspace of each operation mode has been analyzed and geometrically illustrated. It allows us to determine the regions in which the reconfiguration takes place. Furthermore, the inherent self-motion in the Schönflies mode is revealed and illustrated, which occurs at two specified actuated leg lengths. Demonstration of the reconfiguration process and self-motions is provided through a mock-up prototype.

This article presents a novel design of a multisegment shape morphing mechanism that combines a lockable reconfigurable variable geometry truss manipulator (VGTM) with an active parallel compliant mechanism. The structure of the VGTM is in a parallel-serial structure, and its hyper-redundant degree-of-freedom (DOF) can be fully controlled by using two active flexible panels and some lockable joints. This mechanism is suitable for aerospace applications that require light and compact structure with high load-carrying ability as well as achieve multiple DOFs for large-scale shape deformation. To make shape morphing process simple and efficient, the mobility and topological configuration of the mechanism are analyzed first. Then, a control strategy combining the approximate motion mode and the exact motion mode is proposed. The kinematic models for different motion modes are established and solved analytically. It has been found that, under the exact motion mode, two approaches could be realized for the pose control under external loads for each segment. The one with the shorter moving path is selected in this article. Finally, a prototype was constructed to demonstrate the feasibility of this structure and to verify the proposed kinematic model.

BALLET (BALloon Locomotion for Extreme Terrain) is a new concept vehicle for robotic surface mobility on planetary bodies with an atmosphere. The vehicle is composed of a buoyant balloon with six evenly distributed suspended payload modules each serving as a foot for locomotion over inaccessible rugged terrain. While the physics of BALLET will apply on Venus and Mars, the environmental conditions and available component technology limit our consideration to Titan. We describe the concept in detail, its applications for science missions on Titan, mission deployment scenarios, analyses of the concept under varying environmental conditions, and simulations of its locomotion. The concept is shown to be feasible and provides a new approach for exploration of rugged lakes, dunes, shorelines, and cryovolcanic regions on Titan.

Presented in this paper is a method for modeling and simulation of a complete morphing mechanism. The said mechanism has a rigid panel morphing skin that morphs along with a driving mechanism. The said skin is made of segmented panels, inspired by fish scales. Since the gaps between these panels are undesirable, a gapless design is introduced in this paper by using shape-memory polymer (SMP) joints. This paper aims to solve two fundamental problems for the entire system: (1) motion control and (2) force control. The motion control is addressed through the kinematic modeling of two equations including (a) the passive rigid panels and (b) the passive rigid panels to the active mechanism. Force control is achieved through force modeling. This is to develop a relationship of the SMP deformations to the required actuator forces. The experiment is carried out to determine the SMP forces versus deformation, and simulations are conducted to investigate how a complete morphing mechanism behaves. It also reveals that the workspace and singularity of the original mechanism will change after covered by a morphing skin. The developed method sheds light on the design of a complete morphing mechanism.

In this paper, a model is shown to predict the simultaneous deformations occurring when compliant robotic fingers are grasping soft objects. This model aims at providing an accurate estimation of the penetration, internal forces, and deformed shapes of both these fingers and the objects. A particular emphasis is placed on the case when the finger is underactuated but the methodology discussed in this paper is general. Usually in the literature, underactuated fingers are modeled and designed considering their grasps of rigid object because of the complexity associated with deforming objects. This limitation severely hinders the usability of underactuated grippers and either restricts them to a narrow range of applications or requires extensive experimental testing. Furthermore, classical models of underactuated fingers in contact with objects are typically applicable with a maximum of one contact per phalanx only. The model proposed in this paper demonstrates a simple algorithm to compute a virtual subdivision of the phalanges which can be used to estimate the contact pressure arising when there are contacts at many locations simultaneously. This model also proposes a computationally efficient approximation of isotropic soft objects. Numerical simulations of the proposed model are compared here with dynamic simulations, finite element analyses, and experimental measurements which all shows its effectiveness and accuracy. Finally, the extension of the model to other types of underactuated fingers, standard grippers, and fully actuated robotic fingers as well as potential applications is discussed and illustrated.

We proved several theorems about the Rubik’s snake toy, which has a chain-like structure with applications in robot design. These mathematical theories can guide people to design beautiful shapes using the Rubik’s snake. We presented an example for shape design to demonstrate the effectiveness of our approach.

In this study, a numerical framework for joint rotation configuration models of a finger is proposed. The basic idea is to replicate the finger’s geometric posture observed when the human hand grasps a cylindrical object with various cross sections. In the model development, objects with the cross section adopted from the curves of order two (the family of conic sections) are taken into consideration to realize various finger postures. In addition, four different grasp styles, which simulate the individual-specific contact pattern between the surfaces of object and finger, are modeled and applied for the formulation of numerical models. An idea on how to change flexion/extension patterns in the middle of excursion of movement is proposed and discussed. Series of numerical studies have been conducted and analyzed to evaluate the proposed models. From the results, one can see the models’ feasibility and viability as a solution to describing finger’s flexion/extension movements (FEMs) for grasping patterns.

Concentric tube robots (CTRs) have a great potential for use in medical applications. Coupled with a follow-the-leader (FTL) deployment, they allow navigation in constrained environments. However, they are subject to instabilities if one makes use of high curvatures for the tubes, long overlapping lengths of their curved sections, or long transmission lengths. One approach to improve their stability is to pattern the tubes of which they are composed by local removals of material along their lengths. Applying patterns on tubes was proved to be of interest for given deployed lengths of a CTR. In this article, we present a method to enlarge the application field of CTRs that deploy in a follow-the-leader manner, by integrating tube patterning in the design process, with a stability criterion. Our method allows the designer to determine a custom pattern geometry to theoretically ensure the stability of CTRs made of any number of constant curvature tubes, for a complete FTL deployment sequence, and while respecting a desired shape during deployment.

The primary compliance vector (PCV) captures the dominant kinematic behavior of a compliant mechanism. Its trajectory describes large deformation mechanism behavior and can be integrated in an optimization objective in detailed compliant mechanism design. This paper presents a general framework for the optimization of the PCV path, the mechanism trajectory of lowest energy, using a unified stiffness characterization and piecewise curve representation. We present a meaningful objective formulation for the PCV path that evaluates path shape, location, orientation, and length independently and apply the framework to two design examples. The framework is useful for design of planar and shell compliant mechanisms that traverse a specified mechanism trajectory and that are insensitive to load perturbations.

The limited dexterity that existing hand prostheses provide to users contrasts with the manipulation abilities exhibited by state-of-the-art robot hands. This paper presents an underactuated robot hand with in-hand manipulation capabilities to demonstrate the use of underactuation in the development of effective hand replacements. This paper describes a specific underactuated hand architecture, representative of many existing underactuated hand prototypes. First, the hand is modeled and its ability to manipulate objects of different geometries is analyzed. Second, a manipulation strategy suitable for prosthetic applications is proposed. The strategy enables the hand to manipulate objects in-hand without any a priori information of their geometry or physical properties. Finally, experimental tests conducted to validate the theoretical results are presented.

The shape prediction of tendon-driven continuum manipulators is a challenging problem due to the effect of inner friction and external force. Many researchers use actuation displacement or actuation force as model input to predict the shapes of manipulators, but very few consider their relations and models able to predict the status of friction. This paper proposes a model-based method that combines the mechanics model with the kinematic model to predict the shapes of planar single-segment manipulators with consideration of external force and friction. Finally, the shape prediction of manipulators is converted to an optimization problem with actuation displacement and actuation force as the inputs of our algorithm. The distribution of tendon force and the situation of friction can be calculated by using the feedback data of the actuation unit even when actuation direction changes and hysteresis occurs. Experimental results indicate that the method has good performance in predicting the manipulator’s shapes.