Compliant Joints Research Articles

Compliant joint to reduce docking loads between CubeSats

This paper presents the design, modelling and experimental verification of a damping joint for application to miniature space docking mechanisms. The joint design is based on deformable elastomeric elements, thus avoiding any sliding or contact between moving components. Numerical FEM simulations have been conducted in order to quantify the joint mechanical characteristics (rigidity and damping coefficient) as a function of the main design parameters (geometry, material, assembly). The obtained parametric relations provide an estimate of the joint characteristics based on the selected design. An equivalent visco-elastic model is developed and implemented in dynamic simulations. The results of the experimental evaluation of the joint design provide a validation of the developed models and prove the advantage of adopting damping joints in docking applications between small satellites, like reduced contact loads and enhanced damping.

Modelling the joint rotational compliance of stud-pocket type flight inter-section joint

Joint rotational compliance (JRC) of a flight intersection joint (FIJ) is an important parameter in the structural design and analysis of a launch vehicle. The JRC is always quantified through extensive experiments due to the non-availability of a reliable theoretical or numerical model. This paper attempts to bring out an analytical model based on the modelling of localised component joint stiffness. The local component joint stiffness is modelled and quantified through numerical methods and verified through experiments. The analytically predicted JRC for a typical FIJ is compared with that obtained from independent numerical modelling of the full FIJ based on finite element analysis, where a very good agreement is observed between analytical and FEA results. Further, the effect of pre-tightening of studs and variations in size and number of studs and their combinations on the JRC of a FIJ is investigated. It has been demonstrated that (1) the pre-tightening of studs enhances the JRC to an extent of 30% to 10% when loading is increased from no load to the first yield moment; and (2) the increase in the number of studs for a given stud size results in significantly enhanced JRC as compared to the increase in the size of studs.

MECHANICAL JOINTS IN ROLLED SCREW-THREADED REINFORCING BARS

Introduction. Russian manufacturers currently produce screw-threaded reinforcing bars (rebars) and couplers to join them. However, the application of such reinforcement in the construction industry is hindered by a high compliance in screw couplings.Aim: to assess the compliance of coupling joints reinforced with adhesives.Materials and methods. The study used Av500P screw-threaded rebars, couplers, as well as adhesive compounds containing a cement binder and epoxy resin. The compounds were injected into the coupling cavity by means of hand pumps, followed by their natural hardening. The tests were conducted using universal testing machines.Results. In terms of strength, yield, and delaminatability, the compounds were found to meet the required stress-strain properties of couplers. Recommendations for assembling joints are provided.Conclusions. The conducted studies show that Av500P screw-threaded rebars can be joined by means of couplers in construction.

A Modeling Method for a 6-SPS Perpendicular Parallel Micro-Manipulation Robot Considering the Motion in Multiple Nonfunctional Directions and Nonlinear Hysteresis

Abstract Precision motion systems that call for an ultrahigh resolution are widely used in ultrahigh-precision engineering applications. In this article, a 6-SPS perpendicular compliant parallel micro-manipulation robot is presented. It is difficult to establish the mapping relationship between the applied voltage and end-effector pose due to the existence of compliant joints and piezoelectric actuators. A modeling method for a 6-SPS perpendicular compliant parallel micro-manipulation robot considering the motion in nonfunctional directions and hysteresis effect is proposed to reflect the characteristic from input voltage to output pose. The motion of the spherical compliant joint is regarded as a spatial six degrees-of-freedom mechanism. This method considers the motion errors in multiple nonfunctional directions of the compliant joints. The internal force and torque are also taken into account based on the spatial force and moment balance condition. The slow, fast dynamic modes, and hysteresis nonlinearity behavior are described using a series and parallel hybrid model structures. The kinematic model and compliance model without considering the motion in nonfunctional directions are conducted for comparison. Simulation results show that the presented modeling method has higher modeling accuracy. Finally, experiments on a 6DOF compliant parallel micro-manipulation robot reveal the fine modeling performance of the developed method for the precision motion systems in the presence of intrinsic hysteresis effect and motion error of compliant joints.

Design and Evaluation of a Balanced Compliant Laparoscopic Grasper.

In laparoscopic surgery, quality of haptic feedback is reduced compared to conventional surgery, leading to unintentional tissue damage during grasping. From the perspective of haptics, poor mechanical design of laparoscopic instrument joints induces friction and a nonlinear actuation-tip force relation. In this study, a novel laparoscopic grasper using compliant joints and a magnetic balancer is presented, and the reduction in hysteresis and friction is evaluated. The hysteresis loop of the novel compliant grasper and two conventional laparoscopic graspers (high quality leading commercial brand and low quality unbranded grasper) were measured. In order to assess quality of haptic feedback, the lowest grasper tip load perceivable by instrument users was measured with the novel and the conventional laparoscopic graspers. The hysteresis loop measurement yielded a mechanical efficiency of 43% for the novel grasper, compared to- 25% and 23% for the Aesculap and the unbranded grasper, respectively. The forces perceivable by the user through the novel grasper were significantly lower (mean 1.37N, SD 0.44N) than those of conventional graspers (mean 2.15N, SD 0.71N and mean 2.65N, SD 1.20N, respectively). The balanced compliant grasper technology has the ability to improve the quality of haptic feedback compared to conventional laparoscopic graspers. Research is needed to relate these results to soft and delicate tissue grasping in a clinical setting, for which this instrument is intended.

A Kinematically Constrained Kalman Filter for Sensor Fusion in a Wearable Origami Robot

AbstractSensing for wearable robots is an ongoing challenge, especially given the recent trend of soft and compliant robots. Recently, a wearable origami exoshell has been designed to sense the user’s torso motion and provide mobility assistance. The materials of the exoshell contribute to a lightweight design with compliant joints, which are ideal characteristics for a wearable device. Common sensors are not ideal for the exoshell as they compromise these design characteristics. Rotary encoders are often rigid metal devices that add considerable weight and compromise the flexibility of the joints. Inertial measurement unit sensors are affected by environments with variable electromagnetic fields and therefore not ideal for wearable applications. Hall effect sensors and gyroscopes are utilized as alternative compatible sensors, which introduce their own set of challenges: noisy measurements and drift due to sensor bias. To mitigate this, we designed the Kinematically Constrained Kalman filter for sensor fusion of gyroscopes and Hall effect sensors, with the goal of estimating the human’s torso and robot joint angles. We augmented the states to consider bias related to the torso angle in order to compensate for drift. The forward kinematics of the robot is incorporated into the Kalman filter as state constraints to address the unobservability of the torso angle and its related bias. The proposed algorithm improved the estimation performance of the torso angle and its bias, compared to the individual sensors and the standard Kalman filter, as demonstrated through bench tests and experiments with a human user.

Impedance Control of a Delta Robot

A delta robot is an attractive platform for robotic applications involving contacts and collisions, such as object assembly, because of its low mass and inertia (for low impedance and high speed), low link and joint compliance (for precision), and mechanical simplicity (for low cost). For these types of applications, impedance control is desirable, enabling a task-level controller to modulate the manipulator impedance to minimize the transfer of energy, momentum and force between the manipulator and the environment or task. In this paper, a feedback linearizing control law in task space is derived and used to construct an impedance controller for a three degree of freedom delta robot. Because the robot is a complex closed chain, neither the forward kinematics nor the feedback linearizing control law can be expressed analytically, in closed form. However we show that both can be computed algorithmically. We also show how tactile sensors, integrated into the gripper, may be used in an outer loop feedback to modify, and specifically reduce, the robot impedance. This is useful for manipulating objects of relatively low mass, or where transfer of energy, momentum or force from the robot to an object to be grasped must be minimized. We demonstrate the controller in simulation for a soft grasping primitive, and also in a laboratory experiment, where it plays speed chess.

Double-spiral: a bioinspired pre-programmable compliant joint with multiple degrees of freedom.

Geometry and material are two key factors that determine the functionality of mechanical elements under a specific boundary condition. Optimum combinations of these factors fulfil desired mechanical behaviour. By exploring biological systems, we find widespread spiral-shaped mechanical elements with various combinations of geometries and material properties functioning under different boundary conditions and load cases. Although these spirals work towards a wide range of goals, some of them are used as nature's solution to compactify highly extensible prolonged structures. Characterizing the principles underlying the functionality of these structures, here we profited from the coiling-uncoiling behaviour and easy adjustability of logarithmic spirals to design a pre-programmable compliant joint. Using the finite-element method, we developed a simple model of the joint and investigated the influence of design variables on its geometry and mechanical behaviour. Our results show that the design variables give us a great possibility to tune the response of the joint and reach a high level of passive control on its behaviour. Using 3D printing and mechanical testing, we replicated the numerical simulations and illustrated the application of the joint in practice. The simplicity, pre-programmability and predictable response of our double-spiral design suggest that it provides an efficient solution for a wide range of engineering applications, such as articulated robotic systems and modular metamaterials.

Interlaminar shifts of two-layer aggressive-resistant combined plates based on metal and fiberglass

In this work, the stress and deformation states of plates made of metal layers wrapped with composite materials in the inner or outer layers were studied. The main goal of this research is to create durable, long-lasting and aggressive environment-resistant structures that can easily bear external dynamic and static loads. The work used the Navier method to study the effects of interlayer displacement. It was found that the lower the modulus, the greater the effect of joint compliance on the deformation of laminated composite plates. A regularity has been established that the greater the thickness of the bearing fiberglass layer, the less the effect of the shear modulus of the seam on the stresses and deformability of two-layer combined slabs. A regularity has been established, the greater the thickness of the bearing metal layer, the less the effect of the shear modulus of the seam on the stresses and deformation of two-layer combined plates.

Online Cartesian Compliance Shaping of Redundant Robots in Assembly Tasks

This paper presents a universal approach to shaping the mechanical properties of the interaction between a collaborative robot and its environment through an end-effector Cartesian compliance shaping. More specifically, the focus is on the class of kinematically redundant robots, for which a novel redundancy reconfiguration scheme for online optimization of the Cartesian compliance of the end-effector is presented. The null-space reconfiguration aims to enable the more efficient and versatile use of collaborative robots, including robots with passive compliant joints. The proposed approach is model-based and gradient-based to enable real-time computation and reconfiguration of the robot for Cartesian compliance while ensuring accurate position tracking. The optimization algorithm combines two coordinate frames: the global (world) coordinate frame commonly used for end-effector trajectory tracking; and the coordinate frame fixed to the end-effector in which optimization is computed. Another attractive feature of the approach is the bound on the magnitude of the interaction force in contact tasks. The results are validated on a torque-controlled 7-DOF KUKA LWR robot emulating joint compliance in a quasi-static experiment (the robot exerts a force on an external object) and a peg-in-hole experiment emulating an assembly task.

Comparative folding/unfolding performance of notch-type compliant joints

Origami design has been a popular research field for decades, generating inspiration for various structural applications. The shift from paper to more practical materials such as plate-like metals is materialized by surrogate folds such as compliant hinges. Therefore, it is critical to explore the kinematic and dynamic characteristics of these joints. In this paper, a comparative numerical study of the folding/unfolding performance of three notch-type compliant joints, namely groove, elliptical holes, and rectangular holes is presented. Indicators including stress contour, load-deformation, moment-angle, and stiffness-angle are selected to evaluate the performance of joints with different geometric parameters, especially the hysteretic behaviors of the joints. The results illustrate that the geometric parameters of the plate and joint are well correlated with these performance indicators. The transition behaviors of the folding/unfolding stiffness of all joints are associated with a certain regime of rotational angles. Besides, the performances of all studied joints are benchmarked against the much-popularized outside LET joint, from which their deformation modes are recognized. Finally, considering various performance aspects, the groove joint is recognized as the most suitable for the folding of a planar plate.

Mechanical Compliance and Dynamic Load Isolation Design of Lower Limb Exoskeleton for Locomotion Assistance

Improving the comfort and portability of exoskeleton structures for human locomotion assistance is challenging. Research shows that the misalignments between exoskeletons and human joints will lead to interference and undesired interaction forces in locomotion. Moreover, the weight and inertia of exoskeletons will lead to rapid changes in impact forces acting on the wearer. When the exoskeleton is tightly bound to the wearer’s body, such forces are usually unavoidable. These issues not only reduce the comfort and portability of exoskeletons, but also increase the energy costs to wearers. To address these issues, we propose a novel lower limb exoskeleton with a constant-force suspension mechanism and self-adapting compliant joints. The constant-force suspension mechanism aims to isolate the impact force on the back of the wearer, while the self-adapting compliant joints aim to reduce the misalignments between the exoskeleton and the wearer. For the first time, a structure designed to isolate the impact force of exoskeletons is proposed. Moreover, compliant joints exhibiting comprehensive great performances in portability, flexibility, self-aligning, and weight-supporting ability have also been rarely reported. The experimental results demonstrate that the developed mechanisms can reduce the impact forces and misalignments in locomotion. Furthermore, the proposed exoskeleton can reduce the metabolic rate during walking at 5 km/h by 10.95 <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\pm$</tex-math></inline-formula> 4.40% and that during running at 9 km/h by 1.71 <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\pm$</tex-math></inline-formula> 4.54% compared with locomotion without the exoskeleton. These results confirm that the proposed designs can improve the performance of the exoskeleton in locomotion.

A wrist-inspired suspended tubercle-type tensegrity joint with variable stiffness capacity

In complex and unpredictable environments or in situations of human–robot interaction, a soft and flexible robot performs more safely and is more impact resistant compared to a traditional rigid robot. To enable robots to have bionic features (flexibility, compliance and variable stiffness) similar to human joints, structures involving suspended tubercle tensegrity are researched. The suspended tubercle gives the joint compliance and flexibility by isolating two moving parts. The variable stiffness capacity is achieved by changing the internal stress of tensegrity through the simultaneous contraction or relaxation of the driving tendons. A wrist-inspired tensegrity-based bionic joint is proposed as a case study. It has variable stiffness and two rotations with a total of three degrees of freedom. Through theoretical derivation and simulation calculation in the NASA Tensegrity RobotToolkit (NTRT) simulator, the range of motion, stiffness adjustable capacity, and their interaction are studied. A prototype is built and tested under a motion capture system. The experimental result agrees well with the theoretical simulation. Our experiments show that the suspended tubercle-type tensegrity is flexible, the stiffness is adjustable and easy to control, and it has great potential for bionic joints.

The compliant version of the 3-RRR spherical parallel mechanism known as “Agile-Eye”: Kinetostatic analysis and parasitic displacement evaluation

The compliant version of the 3-RRR (R - revolute joint) spherical parallel mechanism known as “Agile-Eye” is presented. The kinetostatic analysis of this Compliant Spherical Parallel Mechanism (CSPM) is conducted using the Compliance Matrix Method (CMM) evaluating two different types of Rotational Compliant Joints (RCJs) and with three inputs. These independent inputs could be forces or displacements. Expressions that relate the input forces/displacements with the displacement of the moving platform are obtained from the kinetostatic analysis. These expressions are used to obtain the required inputs to perform a rotational trajectory of the moving platform; parasitic displacements are computed during this process. Analytical results are validated through Finite Element Analysis (FEA). Additionally, the CSPM geometric parameters-parasitic displacements relation is characterized. Those parameters resulting with lower parasitic displacements are determined. Finally, expressions from the kinetostatic analysis are corroborated experimentally using input displacements in a manufactured prototype with parameters selected to have reduced parasitic displacements. Results from the FEA-simulations and experimental tests demonstrated that the expressions obtained from the kinetostatic analysis can accurately describe the force–displacement relations of the proposed CSPM.

Modeling and Verification for a Three-Degree-of-Freedom Flexure-Based Planar Parallel Micro Manipulator

Abstract Micro positioning systems are popular devices to achieve ultrahigh precision motion. In this paper, a three-degree-of-freedom (3-DOF) flexure-based planar parallel micro manipulator is presented. The existing literature focusing on the modeling of micro manipulator is difficult to fully reflect the real internal physical characteristic in the relationship between the input voltage and output pose. A new comprehensive nonlinear model for a three-DOF flexure-based planar parallel micro manipulator considering the errors of compliant joint in multiple non-functional directions, inherent force, moment, and nonlinear properties of the piezoelectric actuator is proposed. The ideal kinematic model and stiffness model are derived for comparison to verify the comprehensive nonlinear model. The simulation results show that the accuracy of the comprehensive nonlinear model is higher than that of other two models. Finally, the experimental results demonstrate that the average accuracy of the proposed modeling method in the translational direction is 26.35% better than that of the ideal kinematic model. The average accuracy in the rotational direction is 27.49% better than that of the ideal kinematic model. The proposed comprehensive nonlinear model can improve the modeling accuracy. It can be applied to other types of flexure-based micro manipulator.

Compression and tension tests of wooden elements with glued steel plates

The use of classical elements in spatial structures of prefabricated buildings is inefficient due to a design complexity and specific quantity of metal in the assembled components. The paper studies the durability, stability and deformability of wooden elements with glued metal plates working in a multiply connected structure under compressive and tensile loads. The experiment series include maximum loads causing the loss of stability and destruction of prototypes as well as deformation of wooden and metal elements. As a result, the dependences are suggested for the carrying capacity of elements on the load type, thickness and depth of the glued steel plate, and the dependence of tension and compression of elements on the efforts. The latter can be applied in calculations under the strain scheme and modeling of the joint compliance of the multiply connected structure.

Compliant universal joint with preformed flexible segments

Compliant universal joint with preformed flexible segments

Development of a High-Speed Swimming Robot With the Capability of Fish-Like Leaping

Achieving fast and agile swimming still remains extremely challenging for a self-propelled robotic fish due to the constraint of actuator’s propulsion capability. In this article, we report an untethered bioinspired robotic fish, which combines a high-frequency oscillation and a compliant passive mechanism to realize fast swimming, high pitch maneuvers, and even the leaping motion. For pursuing the explosive propulsion of the robotic fish, we propose an actuation system with a powerful output and a compact structure. A dynamic model is established and indicates that the compliant joint is able to modulate the power transmitted to a caudal fin to affect its velocity in the return stroke for generating more peak thrust. The design is validated with extensive experimental results. Namely, the robotic fish can surprisingly reach up to a speed of 3.8 body lengths per second (BL/s). Compared to the case with a rigid joint, dramatic improvements, involving a speed of 1.2 BL/s and a swimming distance of 141.2 m (70.6%), have been obtained, which reveal that besides the high-frequency oscillation, the compliant passive mechanism is also of great significance to perform high-speed swimming. Additionally, the robotic fish demonstrates its high pitch maneuvers by performing an agile front flip motion with a radius of 0.4 BL and an average angular velocity of 439 <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$^\circ$</tex-math></inline-formula> /s. Most importantly, with a simple control strategy, our robotic fish can remarkably leap out of water completely. Results from this study provide significant insights into the innovative designs of next-generation robotic fishes, which require high speed and maneuverability.

Wave-Shaped Notched Compliant Joint With High Rigidity

Notched compliant joints (NCJs) have been widely used in orthopedic surgeries requiring large curvatures for a minimally invasive approach to lesions and high rigidity for cutting hard tissues. With current NCJ designs, there is a trade-off between maximizing rigidity and maximizing curvature for a specified constrained size. Considering notch geometry, larger sizes of notch gaps lead to greater curvatures, however, smaller spacing between notches decreases rigidity. Herein, we propose an NCJ with a novel notch shape, such that the gap of the spacer can be increased without changing that of the notch. Furthermore, we determined the best design parameters for achieving the maximum rigidity for a given driving force. The higher rigidity of the proposed NCJ compared with that of general NCJs is shown through a simulation and experiments. The difference in rigidities between the proposed and general NCJs was 66% with the p-value of <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$5.68 \times {10}^{ - 9}$</tex-math></inline-formula> in a 95% confidence interval which was found to be a statistically significant improvement. In a cutting test, while keeping the curvature, the proposed NCJ increased the cutting amount compared with general NCJs. We verified that the proposed NCJ can achieve both high rigidity and large curvature. The main feature of this study is the development of an NCJ in which both the gap of the spacer and the gap of the notch can be independently changed without affecting each other. The proposed NCJ achieves improved rigidity without loss of curvature.

Characterization of milling robot mode shape and analysis of the weak parts causing end vibration

The existing studies on milling robot dynamic characteristics pay little attention to robot structures, while structure mode shape analysis is significant to accurate vibration control. This paper applies the 3D scanning laser Doppler vibrometer to the milling robot, and proposes the R2-based compliance identification criterion to identify the robot deformation parts as the joints, greatly reducing the number of degrees-of-freedom (DOF) required for the mode shape characterization. Then, the multi-joint and full-DOF mode shape (MFMS) is proposed to succinctly characterize the robot mode shape by mapping the vibrations of numerous measurement points to the joints. MFMS shows that, different from the conventional studies, it is necessary to consider the robot joint compliance in multiple DOFs. For example, in this paper, all the 6 joints are deformed in the first two mode shapes, while the last 3 joints are deformed in the rotational DOFs in the 3 ∼ 6 mode shapes. Based on MFMS, the weak excitation direction at tool center point (TCP) is analyzed and the TCP amplitude is successfully predicted to be almost halved after changing the milling force direction. The weak joint-DOF dominating TCP vibration is analyzed, and it is found that there are only a few weak joint-DOFs in each mode and they vary with the mode, which is instructive for accurate vibration suppression and joint enhancement.