We propose a method for designing targeted 3D polygonal models that can be folded flat, which consist of side panels as well as horizontal top and bottom panels. Vertically adjacent panels are connected by hinges at their horizontal edges. The models can be folded flat by pushing down the top panel, while they can be also deployed by pulling up the top panel. The key idea in making the model so that it can be folded flat is to add vertical slits along the edges of side panels; the horizontally adjacent side panels are separated in the folded state, and are connected to form a closed solid model in the deployed state. Our method takes the shapes of the top panel as well as the cross sections of the side panels as inputs. Users of our prototype system first simply draw the top panel as a convex polygon. They then draw polylines to specify the cross sections. Since the polyhedral model generated by the input data rarely satisfies flat-foldability conditions, our system modifies the positions of the vertices in cross sections based on numerical optimization. Unlike most origami design systems that ignore material thickness, our system can output the 3D geometry of panels so that they can be used to form a closed 3D model with a certain thickness.

There are many excellent graded structures existing in nature to optimize the mechanical properties in various load situations by adjusting the distribution of materials. In this research, rigid origami and graded structure concept are combined together to form the graded origami structures. Seven methods are proposed, including changing the length of crease lines, changing the sector angle, changing the number of units, and the combinations of them. Two rigid origami patterns, Miura-ori and Arc-Miura, are chosen to generate the graded origami structures, and the geometric parameters of each pattern are studied. For engineering application, quasi-static three-point bending response of sandwich beams with graded Miura-ori core based on changing the number of units and changing both the length of crease lines and the sector angle is explored. The investigation reveals that sandwich beams with graded Miura-ori core have preferable energy absorption capability in this load situation compared with the normal Miura-ori core.

This paper proposes the use of passive force and torque limiting devices to bound the maximum forces that can be applied at the end-effector or along the links of a robot, thereby ensuring the safety of human-robot interaction. Planar isotropic force limiting modules are proposed and used to analyze the force capabilities of a two-degree-of-freedom planar serial robot. The force capabilities at the end-effector are first analyzed. It is shown that, using isotropic force limiting modules, the performance to safety index remains excellent for all configurations of the robot. The maximum contact forces along the links of the robot are then analyzed. Force and torque limiters are distributed along the structure of the robot in order to ensure that the forces applied at any point of contact along the links are bounded. A power analysis is then presented in order to support the results. Finally, examples of mechanical designs of force/torque limiters are shown to illustrate a possible practical implementation of the concept.

The kinematics, instantaneous motion, and statics of a manipulator have recently been determined algebraically. In the past, such studies did not provide any intuition about the equation. Robot designers had to use a numerical method or trial-and-error solver with unintuitive equations. Alternatively, all algebraic processes have their own geometrical meaning. Geometric analysis provides intuition for designing the linkages of a robot. Screw theory and barycentric formulas are used to find meaningful geometric measures. The kinematics and statics of a manipulator are described by an axis screw and its reciprocal line screw. The barycenter of a triangle with edges and a perpendicular distance between the two screws are useful geometric measures for geometric analysis. This study provides a geometric interpretation of the kinematics and statics of a planar manipulator using a barycentric formula.

In this paper, a novel geometric model for a planar slider-crank mechanism is established to quantify the position uncertainty of a coupler point caused by joint clearances. The clearance of each revolute and prismatic joint is characterized by a short clearance link. The prismatic joint with clearance is modeled as a link with infinite link length and a variable short link. The linkage with joint clearance is thus modeled as one with redundant freedom. The uncertainty is the result of the redundancy and the extremity of the redundancy is determined through Ting’ N-bar rotatability laws.

We present the design for a family of deployable structures based on the origami flasher that are rigidly foldable, i.e., foldable with revolute joints at the hinges and planar rigid faces, and that exhibit a single degree of freedom in their motion. These structures may be used to realize highly compact deployable mechanisms.

Design of automatic gear boxes with better performance is a pursuit goal of the modern automobile industry. In order to develop CAD method for the creative design of automatic gear boxes, this paper proposes an automatic method for the structure synthesis of one degree of freedom (DOF) epicyclic gear trains (EGTs) with one main shaft which serve as the key mechanisms in automatic gear boxes. First, based on the graph representation of EGTs, the canonical perimeter graphs and the corresponding canonical adjacency matrices are obtained. Then, based on the canonical adjacency matrices, the characteristic number strings are obtained and used to identify isomorphism in the synthesis process. Third, an automatic method is proposed to generate the basic graphs of the topological graphs of EGTs, and the basic graphs up to 9 links are synthesized. After that, based on the structural characteristics for the graphs of EGTs, an automatic method is proposed to synthesize the topological graphs of EGTs from the basic graphs, and an algorithm for the detection of rigid subchains in EGTs is also presented. Finally, a program is developed, and 1-DOF EGTs having one main shaft with up to 9 links are synthesized.

Reconfigurable structures based on origami design are useful for multi-functional applications, such as deployable shelters, solar array packaging, and tunable antennas. Origami provides a framework to decompose a complex 2D to 3D transformation into a series of folding operations about predetermined fold lines. Recent optimization toolsets have begun to enable a systematic search of the design space to not only optimize geometry, but mechanical performance criteria as well. However, selecting optimum fold patterns for large folding operations is challenging as geometric nonlinearity influences fold choice throughout the evolution. The present work investigates strategies for design optimization to incorporate the current and future configurations of the structure in the performance evaluation. An optimization method, combined with finite element analysis, is used to distribute mechanical properties within an initially flat structure to determine optimal crease patterns to achieve desired motions. Out-of-plane and twist displacement objectives are used in three examples. The influence of load increment and geometric nonlinearity on the choice of crease patterns is studied and appropriate optimization strategies are discussed.

Development of a mechanism with dual remote center of motion (dual-RCM mechanism) intended for teleoperated ophthalmic surgery is reported in this paper. First, characteristics of RCM mechanisms are analyzed. Then, a method to synthesize dual-RCM mechanisms is proposed. Further the mechanical design parameters are optimized to synthesize types of mechanisms meeting functional requirements as well as workspace constraints. The dual-RCM mechanism intended for teleoperated ophthalmic surgery includes two end-effectors: one provides the tool insertion, the other tracks eye movement. The superiority is embodied in the self-synchronized motion of double end-effectors, which allows RCM point of the working instrument to track the penetration point real-time, thereby enhancing microsurgical accuracy. In the proposed implementation, a conceptual helmet mechanical architecture integrating surgical tools with triple-parallelogram linkages is introduced to release the surgeon’s hands by enabling more robotic technologies during the procedures. The vision of the research is to help revolutionize the ophthalmic surgical procedures from bimanual fashion to master-slave teleoperation.

A method is presented utilizing networks of lamina emergent joints, known as lamina emergent arrays, to accommodate large-curvature developable structures that are also deployable. By exploiting the ruling lines in developable surfaces, this method enables developable structures that can be manufactured with two-dimensional geometry and yet have a greater range of elastic motion than is possible with a solid sheet of material. A mathematical model is developed to describe the resulting stiffness of the structure employing the lamina emergent arrays and equations are derived to facilitate stress analysis of the structure. Finite element results show the sensitivity of alignment of the elements in the array to the stress present in the developed structure. A specific technique for creating an array pattern for conical developable surfaces is described. Examples of developable structures, including curved-fold origami models transitioned to thick materials, are also examined.

This paper presents a novel mechanical design of a lower mobility remote center compliance linkage. This mechanism consists in three platforms connected by three legs with universal joints. Two of these platforms are attached to the ground while last one is the mobile platform. Using screw theory, it is first demonstrated that this mechanism allows its mobile platform to rotate around a fixed point in space without having a joint directly connected to this point. Indeed, knowing the mobility of the two former platforms, it is possible to define a wrench system for each leg and thus, find the reciprocal twist system of the mobile platform. Then, the results of the optimization of the mechanism’s design through a genetic algorithm is presented using the conditioning of its Jacobian matrix as a criterion. Finally, a compliant version of the mechanism is developed and a finite element analysis (FEA) simulation demonstrates the proper mobility of the system under typical loading scenarios.

Origami can be a source of inspiration for rapidly deployable, rigid wall shelters. Folding panels comprised of sandwich panels will result in a lightweight, transportable design. The design of connections between panels is critical to the overall structural performance, but can pose a major design challenge. This paper investigates the implementation of hinges for connections between panels. A single panel, comprised of fiber-reinforced polymer faces and a foam core, is restrained by aluminum hinged connectors and subjected to a uniform load. An exhaustive parametric study is performed using a numerical model previously validated by experimental data. The numerical study will facilitate better understanding of the impact of the 1) number, 2) size, and 3) relative placement of connectors on panel behavior, with data comparisons focusing on the longitudinal surface strains and displacements of the panel. This investigation culminates in a set of guidelines for hinged connectors in origami-inspired structures.

In this paper, we represent a preliminary work towards the design of compliant mechanisms for human safe co-robots. We developed a shape optimization framework for design of planar compliant links for inherently safe robotic manipulators. It is well known intentionally introducing compliance to mechanical design can increase safety of robots. However traditional approaches such as elastic joints or uniform compliant links, were either at the cost of significantly reduced performance or with increased extra complexity and cost. Here, we propose a novel method to design compliant robotic links with a safety constraint which is quantified by Head Injury Criterion (HIC). The robotic links are modeled as a 2D beam with a variable width. Given a safety threshold i.e. HIC constraint, the width of the beam is optimized to give a uniform distribution of HIC along the longitudinal direction of the link. Links with a uniform HIC distribution have a better control performance. Finally, this solution is validated by an huamn-robot impact simulation program built in Matlab.

This article presents the kinematic synthesis of Watt II six-bar mechanisms for simultaneously guiding two bodies through four prescribed positions. The two bodies to be moved are connected by a revolute joint and the motion generation task is defined by the four desired positions of one body and the relative angle of the second body with respect to the first body. The methodology uses an algebraic geometry formulation of the exact synthesis of planar RR dyads for four prescribed positions from classical Burmester theory. The result is a dimensional synthesis technique for designing Watt II mechanisms for four simultaneous positions. A case study illustrating the application of the synthesis algorithm is included.

Self-folding origami has the potential to be utilized in novel areas such as self-assembling robotics and shape-morphing structures. Important decisions in the development of such applications include the choice of active material and its placement on the origami model. With proper placement, the error between the actual and target shapes can be minimized along with cost, weight, and power requirements. Through the incorporation of dynamic models of self-folding origami mechanisms into an optimization routine, optimal orientations for magnetically-active material are identified that minimize error to specified target shapes. The dynamic models, created using Adams 2014, are refined by improvements to magnetic material simulation and more accurate joint stiffness characterization. Self-folding dynamic models of the waterbomb base and Shafer’s Frog Tongue are optimized, demonstrating the potential use of this process as a design tool for other self-folding origami mechanisms.

Origami-inspired engineering provides engineers with new means for creating complicated three-dimensional structures through use of folding and fold-like operations. Motivated by the vision of origami engineering, we have created and modeled a reconfigurable self-folding sheet based on a laminate structure of shape memory alloy (SMA) surrounding a layer of elastomer. Folding behavior is achieved by activating an SMA layer through localized heating. In prior work, we demonstrated localized control of such a sheet using PID and On/Off type feedback controllers. The implementation of these control strategies requires several workarounds to deal with the highly nonlinear and hysteretic behavior of the SMA-based laminate sheet. In the current work, we use a reinforcement learning algorithm to learn control policies that better handle these aspects of the sheet behavior. We perform learning on a reduced order model of the sheet developed based on classical laminate plate theory. This significantly reduces computational costs compared to more complicated finite element modeling options. We demonstrate the effectiveness of the learned control policies in several folding scenarios on the reduced order model. Our results show that reinforcement learning can be a useful tool in feedback control of SMA-based structures.

In this work a novel and general method to find the dynamic balancing conditions, based on the use of Natural Coordinates, is introduced. The method is efficient and very easy to automate, and can be used to obtain the shaking force and the shaking moment balancing conditions for the linkages in the plane and can be extended for linkages in space, although at this time is presented only for planar systems. These conditions can be interpreted and used for the design of dynamic balanced linkages. The application of the method is demonstrated here by finding the force and moment balancing conditions of a general four-bar mechanism that, although simple, can serve as a didactic example to evaluate the method. The resulting conditions are used to the effective design of reactionless linkages with counterweights and counter-inertias.

The sketching of mechanisms (kinematic chains) shows designers a visual understanding of the interrelationship among links and joints in mechanical design, but sketching of mechanisms in manually in conceptual design stage is time-consuming and inefficient. In this paper, a fully-automatic method for sketching of planar simple and multiple joint kinematic chains is proposed. First, the complete sets of the topological structures (topological graphs and contracted graphs) of both simple and multiple joint kinematic chains are introduced. Then an algorithm for the layouts of the contracted graphs with minimal edge crossings is proposed. Third, the expression set of binary sub-paths derived from a topological graph is obtained for the sketching of the simple joint kinematic chain, and based on the sketching of the simple joint kinematic chains the sketching of corresponding multiple joint kinematic chains is obtained. Finally, both simple and multiple joint kinematic chains with numbers of links and numbers of basic loops are provided in batch as examples to show the effectiveness of the method.

The design of a flapping wing air vehicle is dependent on the interaction of drive motors and wings. In addition to the wing shape and spar arrangement, sizing and flapping kinematics affect vehicle performance due to wing deformation resulting from flapping motions. To achieve maximum payload and endurance, it is necessary to select a wing size and flapping rate that will ensure strong performance and compatibility with drive motor capabilities. Due to several conflicting trade-offs in system design, this is a challenging problem. We have conducted an experimental study of several wing sizes at multiple flapping rates to build an understanding of the design space and ensure acceptable vehicle performance. To support this study, we have designed a new custom test stand and data post-processing procedure. The results of this study are used to build a design methodology for flapping wing air vehicles with improved performance and to highlight system design challenges and strategies for mitigation. Using the methodology described in this paper, we have developed a new flapping wing air vehicle called the Robo Raven II. This vehicle uses larger wings than Robo Raven and flight tests have confirmed that Robo Raven II has a higher payload capacity.

We present an analysis of the compliant kaleidocycle, a mechanism which, unlike other compliant mechanisms, may undergo continuous rotation. We analyze the strain energy characteristics of this mechanism during its motion and show that by varying the stiffness and orientation of the flexures, kaleidocycles may be designed to achieve customizable multistable behavior. These devices may be designed to include up to four distinct stable equilibrium positions and may also include regions of neutral stability.