A compliant mechanism can be constructed by mounting springs at joints of a crank-slider linkage. Different mounting schemes bring changes in the stiffness performance. In this paper, a unified stiffness model is developed for a comprehensive analysis of the stiffness performance. With the model, stiffness behaviors of spring-loaded crank-slider mechanisms are analyzed. Influences of each individual spring on the overall performance are characterized. Based on the analysis, a potential application of constructing mechanisms with desired stiffness behavior in a simple implementation is proposed, which is demonstrated by a constant-torque mechanism and a variable stiffness mechanism.

Compliant mechanisms are typically designed for varying stiffness from nearly zero to rigid. However, targeted design for fine tuning within an application's sensitive range of stiffness remains more desirable for practical implementation in accurate loading or positioning systems. To achieve these various competing objectives a “Generalized Spiral Spring” (GSS) is proposed which achieves small size and other objectives by using a reduced number of parameters as provided by the spiral shape description of the components. An analytical model based on virtual work and curved beam theory is developed for accurate prediction of the stiffness. Moreover, Finite Element (FE) models are also developed for verification of the proposed designs. Multiobjective Design Optimization (MDO) is conducted to maximize the linearity in the stiffness versus control parameter response and improve resolution. The proposed analytical model is validated experimentally and computationally. This approach may be used to achieve finesse by accurate positioning with force control for industrial robots and elegant prostheses.

Origami-based flexible, compliant and bio-inspired robots are believed to permit a range of medical applications within confined environments. In this article, we experimentally demonstrated an origami-inspired deployable surgical retractor integrating controllable stiffness mechanisms that can facilitate safe instrument-tissue interaction in comparison to their rigid counterparts. When controllable negative pressure is applied to the jammed origami structure of the retractor, it becomes more rigid, resulting in an increase in strength. Hence, we examine performances of retractor based on Daler-Rowney Canford paper (38 gsm) and sandpaper of 1000 grits. Experiments on the proposed retractor prototype showed sandpaper-based retractor can outperform paper-38-gsm retractor for tenting the facelift incision with the width of more than 9 cm. Though paper 38 gsm comprised of thin layers 16 times lesser in thickness than sandpaper, the experiments proved its performance comparable to the latter in the context of layer jamming (LJ). We leverage the advantage of LJ mechanism to change the retractor stiffness in an economical way, allowing the instrument to hold and separate the facelift incision to mitigate the likelihood of surgical complications. The retractor was equipped with a custom-made printed conductive ink-based fabric piezoresistive tactile sensor to assist clinicians with tissue-retractor interaction force information. The proposed sensor showed a linear relationship with the applied force and has a sensitivity of 0.833 N-1. Finally, cadaver experiments demonstrate an effective origami-inspired surgical retractor for assistance to surgeons and clinicians in near future.

Silicone-based pneumatic actuators are among the most widely used soft actuators in adaptable fingers. However, due to the soft nature of silicone, the performance of these fingers is highly affected by the low torsional stiffness, which may cause failure in grasping and manipulation. To address this problem, a compact design is proposed by embedding a rigid skeleton into a soft pneumatic finger. A finite element approach with an analysical model is used to evaluate the performance of the fingers both with and without the skeleton. Then, a series of experiments is performed to study the bending motion and rigidity of the fingers. The results reveal that the skeleton increases the torsional stiffness of the finger up to 300%. Furthermore, the consistency with the experimental data indicates the good precision of the proposed modeling method. Finally, a two-finger hand is designed to evaluate the performance of the reinforced finger in reality. The grasp experiments illustrate that the hybrid finger with the skeleton is highly adaptable and can successfully grasp and manipulate heavy objects. Thus, a potential approach is proposed to improve the torsional stiffness of silicone-based pneumatic fingers while maintaining adaptability.

The regional sandwiching of compliant sheets (ReCS) technique presented in this work creates flat-foldable, rigid-foldable, and self-deploying thick origami-based mechanisms. Regional sandwiching of the compliant sheet is used to create mountain-valley assignments for each fold about a vertex, constraining motion to a single branch of folding. Strain energy in deflected flexible members is used to enable self-deployment. This work presents the methods to design origami-based mechanisms using the ReCS technique, including volume trimming at the vertex of the compliant sheet and of the panels used in the sandwich. Three physical models, a simple single fold mechanism, a degree-four vertex mechanism, and a full tessellation, are presented to demonstrate the ReCS technique using acrylic panels with spring and low-carbon steels. Consideration is given to the risk of yielding of the compliant sheet due to parasitic motion with possible mitigation of yielding by decreasing the thickness of the sheet.

Recently, the truss antennas with deployable tetrahedron unit mechanisms have been successfully applied in orbit, owing to the advantages of large calibers, high accuracy, and large folding ratios. As multiloop coupled mechanisms, deployable tetrahedral mechanisms have multiple different output links, whose supporting limbs connecting output links and the base are mutually coupled. These mechanisms are also called the passive-input overconstrained mechanisms because their passive torsion springs are used as drivers and because the number of the drivers contained is more than the degrees of freedom (DOFs). In this work, a method based on the equivalent concept of first link-removing and then restoring is proposed for the DOF analysis of the multiloop coupled deployable tetrahedral mechanisms. With one coupled chain removed, the equivalent serial chains between the coupled components and the base are established in the remainder of the mechanisms. Then, the coupled chain removed is restored and the equivalent of the multiloop coupled mechanisms is obtained. The Lagrange method is used to establish the dynamic equation of the passive-input overconstrained mechanisms; the influence of the stiffness and number of torsion springs on the unfolding motion is examined.

Continuous layer jamming is an effective tunable stiffness mechanism that utilizes vacuum to vary friction between laminates enclosed in a membrane. In this paper, we present a discrete layer jamming mechanism that is composed of a multilayered beam and multiple variable pressure clamps placed discretely along the beam; system stiffness can be varied by changing the pressure applied by the clamps. In comparison to continuous layer jamming, discrete layer jamming is simpler as it can be implemented with dynamic variable pressure actuators for faster control, better portability, and no sealing issues due to no need for an air supply. Design and experiments show that discrete layer jamming can be used for a variable stiffness co-robot arm. The concept is validated by quasi-static cantilever bending experiments. The measurements show that clamping 10% of the beam area with two clamps increases the bending stiffness by around 17 times when increasing the clamping pressure from 0 to 3 MPa. Computational case studies using finite element analysis for the five key parameters are presented, including clamp location, clamp width, number of laminates, friction coefficient, and number of clamps. Clamp location, number of clamps, and number of laminates are found to be most useful for optimizing a discrete layer jamming design. Actuation requirements for a variable pressure clamp are presented based on results from laminate beam compression tests.

Based on the bi-material triangle lattice cell, a new cellular structure, bi-material re-entrant triangle (BRT) cellular structure, is devised to incorporate tailorable coefficient of thermal expansion (CTE) and tunable Poisson's ratio (PR) properties by replacing the straight base of a triangle with two hypotenuse members. A general thermoelasticity equation to systematically build the relationship among the external force, the temperature load, and the deformation for planar lattice structures with bounded joints is derived and then embedded into a theoretical model for the devised BRT structure. Using assembled thermoelasticity equation, effective PR, Young's modulus, as well as CTE are computed. In order to guide designers to construct initial concepts, the design domain for coupling negative CTE and negative PR properties is plotted. The material-property-combination region that can be achieved by this cellular structure is determined within an Ashby material selection chart of CTE versus PR. Nine available combinations of CTE and PR properties are extracted and demonstrated with abaqus simulation.

Patients suffering from stroke need to undergo a standard and intensive rehabilitation therapy. The rehabilitation training consists of three sequential stages: the first stage is controlled joint movement under external actuator, the second stage deals with supporting the movements by providing assistive force, and the last stage provides variety and difficulty to exercises. Most of the exoskeletons developed so far for rehabilitation are restricted to a particular type of activity. Although a few exoskeletons incorporate different modes of rehabilitation, those are software controlled requiring sensory data acquisition and complex control architecture. To bridge this gap, a portable elbow exoskeleton has been developed for delivering three stages of rehabilitation in a single structure without affecting the range of motion and safety features. Use of electric motor and springs have been arranged in the actuation mechanism to minimize the energy consumption. The developed exoskeleton enhances torque to weight ratio compared to existing models, and all the three modes of rehabilitation have been controlled using a single motor.

To reduce injury in physical human–robot interactions (pHRIs), a common practice is to introduce compliance to joints or arm of a robotic manipulator. In this paper, we present a robotic arm made of parallel guided beams whose stiffness can be continuously tuned by morphing the shape of the cross section through two four-bar linkages actuated by servo motors. An analytical lateral stiffness model is derived based on the pseudo-rigid-body model and validated by experiments. A physical prototype of a three-armed manipulator is built. Extensive stiffness and impact tests are conducted, and the results show that the stiffness of the robotic arm can be changed up to 3.6 times at a morphing angle of 37 deg. At an impact velocity of 2.2 m/s, the peak acceleration has a decrease of 19.4% and a 28.57% reduction of head injury criteria (HIC) when the arm is tuned from the high stiffness mode to the low stiffness mode. These preliminary results demonstrate the feasibility to reduce impact injury by introducing compliance into the robotic link and that the compliant link solution could be an alternative approach for addressing safety concerns of physical human–robot interactions.

An increase in the interaction forces/torques at the exoskeleton–human connections due to kinematic mismatches may consequently result in the user discomfort and/or lower performance of the exoskeleton. The stiffness of the exoskeleton–human connection elements plays a key role in this issue. The purpose of this study is to assess the effects of the exoskeleton–human connection stiffness on the user comfort and limb tracking error during normal gait. A biomechanical model of the leg was built and connected to a model of an exoskeleton by elastic connections whose stiffness tensors were identified experimentally for three participants. The effects of the connection stiffness on the gait performance were investigated using two indices: discomfort index (DI) and tracking error index (TEI), which is the difference between the human joint angle and that of the exoskeleton. DI was calculated based on the mechanical energy stored in the elastic connection elements. Although an increase of the stiffness magnitude in every direction results in DI growth, the torsional stiffness of the shank connection was found to be the most sensitive for DI. TEI, on the other hand, showed both increasing and decreasing trends with the stiffness increase in different directions. It was found that there are optimal values for some connection stiffness elements, especially shank connection, possibly due to intricacy of the knee joint, that would improve both DI and TEI. For instance, the decrease of the torsional and mediolateral shank connection stiffness improved DI and TEI by an average of about 50%.

The simultaneous control of force and motion is important in everyday activities when humans interact with objects. While many studies have analyzed the control of movement within a perturbing force field, few have investigated its dual aspects of controlling a contact force in nonisometric conditions. The mechanism by which the central nervous system controls forces during movements is still unclear, and it can be elucidated by estimating the mechanical properties of the arm during tasks with concurrent motion and contact force goals. We investigate how arm mechanics change when a force control task is accomplished during low-frequency positional perturbations of the arm. Contrary to many force regulation algorithms implemented in robotics, where contact impedance is decreased to reduce force fluctuations in response to position disturbances, we observed a steady increase of arm endpoint stiffness as the task progressed. Based on this evidence, we propose a theoretical framework suggesting that an internal model of the perturbing trajectory is formed. We observed that force regulation in the presence of predictable positional disturbances is implemented using a position control strategy together with the modulation of the endpoint stiffness magnitude, where the direction of the endpoint stiffness ellipse's major axis is oriented toward the desired force.

A planar tensegrity manipulator made of two X-mechanisms in series is studied in this paper. Contrary to a classical 2-R linkage, the proposed architecture does not contain elements subject to bending and it can be driven with remote actuation and cables in an antagonistic way. Accordingly, it is an interesting candidate for the design of lightweight manipulators with variable stiffness suitable for safe interactions. On the other hand, its kinematics is more challenging because of a variable instantaneous center of rotation of the X-mechanisms. First, the inverse kinematic problem is solved using an adequate methodology, the singularities are determined, and the workspace shape is analyzed as a function of the design parameters. Then, two actuation schemes are studied and the wrench feasible workspace is analyzed for each of them. The second actuation scheme provides a larger wrench feasible workspace and allows for stiffness control.

Compliant mechanisms find use in numerous applications in both microscale and macroscale devices. Most of the current compliant mechanisms base their behavior on beam flexures. Their range of motion is thus limited by the stresses developed upon deflection. Conversely, the proposed mechanism relies on elastically nonlinear components to achieve large deformations. These nonlinear elements are composite morphing double-helical structures that are able to extend and coil like springs, yet, with nonlinear stiffness characteristics. A mechanism consisting of such structures, assembled in a simple truss configuration, is explored. A variety of behaviors is unveiled that could be exploited to expand the design space of current compliant mechanisms. The type of behavior is found to depend on the initial geometry of the structural assembly, the lay-up, and other characteristics specific of the composite components.

The energy balancing concept seeks to reduce actuation requirements for a morphing structure by strategically locating negative stiffness devices to tailor the required deployment forces and moments. One such device is the spiral pulley negative stiffness mechanism. This uses a cable connected with a pre-tension spring to convert the decreasing spring force into the increasing balanced torque. The kinematics of the spiral pulley is first developed for bidirectional actuation, and its geometry is then optimized by employing an energy conversion efficiency function. The performance of the optimized bidirectional spiral pulley is then evaluated through the net torque, the total required energy, and energy conversion efficiency. Then, an additional test rig tests the bidirectional negative stiffness property and compares the characteristics with the corresponding analytical result. Exploiting the negative stiffness mechanism is of significant interest not only in the field of morphing aircraft but also in many other energy and power reduction applications.

This paper presents a novel three degrees-of-freedom (DOF) compliant parallel mechanism (CPM) with a fully decoupled spatial motion ( θ X − θ Y − Z ) and optimized mechanical properties. To design the CPM using the beam-based structural optimization method, several novel criteria for synthesizing three-legged CPMs with fully decoupled motions are derived. The obtained results suggest that the synthesized CPM delivers a diagonal compliance matrix, a large workspace of 10 d e g × 10 d e g × 7 m m , fast dynamic response of ∼ 100 H z , and good stiffness performance whereby the translational and rotational stiffness ratios are ∼3600 and ∼570, respectively. A prototype of the synthesized CPM is fabricated using one of the three-dimensional (3D) printing technologies, electron beam melting (EBM). Experimental results have shown that the 3D printed CPM can produce the full workspace with deterministic mechanical properties whereby the highest deviations between the theoretical and experimental results are 11.2 % and 1 % for stiffness and dynamic behaviors, respectively. Importantly, the decoupled-motion characteristic is also verified via an energy approach, i.e., the energies of the undesired parasitic motions are minor ( < 1 % ) as compared with the energy of the desired motion. In addition, several comparisons are conducted to clarify the advantages of the synthesized CPM to the existing designs. All these investigations suggest that the proposed CPM can be used in precision positioning systems due to the good stiffness characteristics, large workspace, fast dynamic response, and decoupled output motions.

In this paper, a lightweight high-payload cable-driven serial-parallel manipulator is proposed. The manipulator comprises one 3-degree-of-freedom (3-DOF) shoulder joint and one single-DOF elbow joint. Using a special tension-amplifying principle, which is an ingenious two-stage deceleration method, the proposed manipulator has a higher load/mass ratio than those of conventional manipulators. In this paper, the special tension-amplifying principle is discussed in detail. The shoulder and elbow joints of the proposed manipulator are driven by cables. The design of this cable-driven mechanism and the mobility of the joints are analyzed, and the structural parameters of the joints are optimized to improve the payload capacity. The size of the manipulator is close to that of a human arm because the actuators of the cable-driven mechanism can be rear-mounted. Because the elbow joint is located at the end of the shoulder joint and the driven cables of the elbow joint are coupled with the rotation of the shoulder joint, the manipulator is designed with decoupled cable routing. The overall configuration and cable routing of the manipulator are presented, and then, kinematics, joint stiffness, strength, and workspace of the manipulator are analyzed. Finally, we report on the fabrication of a physical prototype and testing of its joint stiffness, payload capacity, workspace, speed, and repeatability to verify the feasibility of our proposed manipulator.

Parallel robots have been primarily investigated as potential mechanisms with stiffness modulation capabilities through the use of actuation redundancy to change internal preload. This paper investigates real-time stiffness modulation through the combined use of kinematic redundancy and variable stiffness actuators. A known notion of directional stiffness is used to guide the real-time geometric reconfiguration of a parallel robot and command changes in joint-level stiffness. A weighted gradient-projection redundancy resolution approach is demonstrated for resolving kinematic redundancy while satisfying the desired directional stiffness and avoiding singularity and collision between the legs of a Gough/Stewart parallel robot with movable anchor points at its base and with variable stiffness actuators. A simulation study is carried out to delineate the effects of using kinematic redundancy with or without the use of variable stiffness actuators. In addition, modulation of the entire stiffness matrix is demonstrated as an extension of the approach for modulating directional stiffness.

The variable-stiffness joint (VSJ) plays an important role in creating compliant and powerful motions. This paper presents a novel wire-driven VSJ based on a permanent magnetic mechanism (PMM). The proposed joint regulates the joint stiffness with lower energy consumption through a wide range via the permanent magnetic mechanism. This effect possibly depends on the novel nonlinear combination of a permanent magnet-spring and wire-driven system that achieves the same stiffness with lower wire tension. A trapezoidal layout of the joint is proposed. Because of the relationship among the stiffness, the position of the joint and the stiffness of the PMM, the stiffness model is also been established. Based on this model, the decoupling controller is built to independently control the position and stiffness of the joint. Experiments show that the VSJPMM achieves position and stiffness independently and also reduces energy and power required to regulate the stiffness compared with the traditional approach. In addition, the proposed mechanism displays a powerful motion and short stiffness adjustment time.

This paper puts forward a linear variable stiffness joint (VSJ) based on the electromagnetic principle. The VSJ is constituted by an annular permanent magnet (PM) and coaxial cylindrical coil. The output force and stiffness are linearly proportional to the coil current. In consequence, the stiffness adjustment motor and mechanisms required by many common designs of VSJs are eliminated. A physical prototype of the electromagnetic VSJ is manufactured and tested. The results indicate that the prototype can achieve linear force-deflection characteristics and rapid stiffness variation response. Using an Arduino and H-bridge driver board, the electromagnetic compliance control system is developed in order to realize the precise control of the interaction force. The static force control error is no more than ±0.5 N, and the settling time can be controlled within only 40 ms. At last, an experiment of squeezing the raw egg is conducted. The experiment intuitively exhibits the performance of electromagnetic compliance in stable force control and keeping safe robot-environment interaction.