Motion strategy analysis at the pre-bending stage is a fundamental component of underactuated finger grasp research. This study presents the pre-bending motion strategy and corresponding analysis of cable driving forces a 3-DOF underactuated finger comprising cable truss units. This robotic finger uses a tendon-pulley transmission and parallel four-linkage mechanism to realize the grasp capability. The structure and four motion strategies at the pre-bending stage are illustrated. The equivalent joint-driven and quasi-static motion models are established in the case where one or two cable driving forces drive the finger. In accordance with the virtual work principle, the tendon-pulley transmission is transformed into an equivalent joint-driven system. On the basis of the constraints of maximum motion space of the finger, the joint spring stiffness distributions are discussed and the finger quasi-static motion space is analyzed under the condition of single motor driving force. The unique coupled motion process and corresponding cable driving force of the finger driven by a single motor are assessed. Furthermore, three other typical quasi-static motion strategies and their corresponding cable driving forces are discussed. Valid simulation experiments are conducted to verify the accuracy of the quasi-static motion strategy. The analysis of this study can provide guidance and a theoretical reference for the design of cable-driven underactuated hands and control of the couple-driven underactuated mechanism.

This paper presents structures with multiple equilibrium configurations arising from the combination of a state of prestress and unilateral contacts. A design problem is posed where preloaded elastic springs and unilateral constraints are embedded throughout a mechanism. The spring parameters are designed such that multiple target configurations are immobilized due to contact. In each of these configurations, the spring forces maintain compressive reaction forces, immobilizing the structure. Each immobilized configuration can rigidly resist perturbation forces up to some finite magnitude where contact is lost. Hence, this case of multiple configurations in equilibrium due to the combination of prestress and contact is referred to as multi-configuration rigidity. Two examples of structures exhibiting multi-configuration rigidity are presented. First, a four bar linkage with a single kinematic degree of freedom is used to introduce the concept. In the context of the linkage, multi-configuration rigidity is compared to multi-stability, exhibiting the key differences between the two concepts. Then, a 24-degree-of-freedom kirigami surface is presented that can morph between flat and spherical configurations, motivated by RF antenna applications. By embedding torsional springs and fold angle stops throughout the structure, flat and spherical configurations are made rigid. Actuation between the configurations can easily be achieved by snapping the structure between the rigid configurations.

Object throwing is an efficient approach for overcoming the kinematic workspace limitations of robots in placement scenarios. Throwing of objects with rigid link robots has been widely studied in literature. Although using robots with spring-like flexible links can significantly increase the throwing distance, existing contributions are very rare. Therefore, we propose an efficient iterative learning control throwing algorithm and apply it to a flexible link robot. A simple rigid link throwing model is used to generate the motor motion. Errors caused by this simplification are corrected by a flexible link throwing model based on the finite element method. As representative scenario a basketball free throw is selected which requires high throwing accuracy. Here, we demonstrate that the controller can be efficiently pre-learned in simulations to reduce real-world training time. Experiments then validate that our learning control method achieves the required free throw accuracy within very few real-world learning iterations.

Mechanical components, such as springs, dampers and mass, alter and influence an engineered system’s motion based upon a system’s position, velocity and acceleration, respectively. This paper aims to discover and develop another element (dubbed the damper) which provides a force proportional to a system’s jerk (i.e., the derivative of acceleration) to better engineer a system’s response. By utilizing the known applications of jerk in motion planning and control theory, existing possible physical implementations and uses of jerk and the jerk element are discussed in relation to its influence on the system’s response, specifically vibration. Using a Buckingham Pi approach, the theoretical background of the jerk element is presented and possible physical parameters are combined to show how the jerk element could be created from common elements and parameters. The most promising approach of varying the magnetic field of existing magneto-rheological dampers is developed to give an example of the jerk element along with the difficulties and concerns in developing the jerk element. This paper serves less of a purpose towards answering all questions of the jerk element, but rather focuses more on posing the appropriate questions which sets the stage for an easily realizable future jerk element which can improve system performance.

We present an efficient data-driven sparse identification of dynamical systems. The work aims at reconstructing the different sets of governing equations and identify discontinuity surfaces in hybrid systems when the number of discontinuities is known a priori. In our approach, we first focus to identify the switches between the separate vector fields. Then, the dynamics among the manifolds are regressed by making use of the model discovery algorithm of Brunton et al. [1]. The reconstruction of the discontinuity surfaces comes as the outcome of a statistical analysis implemented via symbolic regression with small clusters (micro-clusters) and a rigid library of models. This allows to identify all the many possible switch points that are clustered to determine the actual discontinuity surfaces. The performances of the method are tested on two numerical examples, namely, a canonical spring–mass hopper and a free/impact electromagnetic energy harvester. These applications are characterized by the presence of a single and double discontinuity, respectively. The analyses demonstrate that in the supervised approach, i.e. where the number of discontinuities is preassigned, we are capable to determine accurately both discontinuities and set of governing equations. It is found a great improvement in time of computation reaching the maximum achievable reliability that outperform existing data-driven identification approaches for hybrid systems.

This paper studies a targeted energy transfer (TET) mechanism for a two-degree-of-freedom (TDOF) model in free vibration. The model comprises a primary linear system and a secondary system in the form of an energy sink which can be nonlinear. The free vibrations are considered subject to an impulsive excitation exerted on the primary system, leading to a nonzero initial velocity. The goal is to obtain the spring parameters in the nonlinear energy sink (NES) so as to maximize an energy dissipation measure (EDM) representing the percentage of impulsive energy that is absorbed and dissipated in the NES. A global optimization algorithm is used for this purpose. The optimal performance is assessed for the purely linear, linear-cubic, and purely cubic configurations of the spring connecting the primary and secondary systems. The corresponding results are compared with each other. The optimization process is performed for the EDM averaged over given ranges of the initial impulse and natural frequency in the primary system. It is shown that the type of the optimal configuration can vary depending on these ranges.

The paper reports design and implementation of a Delta Robot based non-anthropomorphic hand. A set of three constant orientation Delta robots are shown to be useful to perform manipulation maneuvers on the object. Voice coil arc actuators are deployed to improve the backdrivability of the robot. The hand consists of three constant orientation fingers which are deployed to grasp an object. The fingers are programmed to behave as a set of springs to generate stable object acquisition. The capability of the robotic hand to perform different maneuvers is demonstrated. The dynamic feedback linearisation method is shown to be useful both for controlling the robotic hand and also to ensure passive grasp of the robotic system. It is shown that the hand can be used to catch an object, improve the grasp forces on the surface of the object, impart oscillatory motion, and also to throw the object in a prescribed direction. Standalone examples are described to suggest the same. The backdrivability of the voice coil arc actuators are demonstrated to be of purpose in improving the passive grasp behaviour of the robot. The swift motion of the actuators are shown to be useful while performing quick oscillations and also to throw the object.

This article presents the actuation strategy of a 2-DOF tensegrity type mechanism that employs three tension springs and a passive universal joint. This mechanism is proposed to be incorporated as an articulation unit for a piping inspection robot in order to overcome pipe bends and junctions. In the event of a junction, external actuations are required to allow the mechanism as well as the robot to follow a certain direction. Using DC-motors coupled with encoders, experiments are carried out on a test bench of the tensegrity mechanism. The actuation of the mobile platform is performed using cables that pass through each spring. By correlating the architecture to a 3-S P S-U parallel mechanism, the singularity-free workspace of the mechanism is analyzed to identify the tilt limits. A closed-loop PID controller is implemented using a microcomputer to perform a linear trajectory within the singularity-free workspace. The Inverse Kinematic Problem (IKP) is solved by passing input tilt angles to the controller. With the help of a force control algorithm, the experiments are carried out under no-load conditions for vertical and horizontal orientations of the mechanism. The error data of the joint positions and the motor torques are then interpreted for both orientations of the mechanism.

Flapping insect wings frequently collide with vegetation and other obstacles during flight. Repeated collisions may irreversibly damage the insect wing, thereby compromising the insect’s ability to fly. Further, reaction torques caused by the collision may destabilize the insect and hinder its ability to maneuver. To mitigate the adverse effects of impact, some insect wings are equipped with a flexible joint called a “costal break.” The costal break buckles once it exceeds a critical angle, which is believed to improve flight stability and prevent irreversible wing damage. However, to our knowledge, there are no models to predict the dynamics of the costal break. Through this research, we develop a simple model of an insect wing with a costal break. The wing was modeled as two beams interconnected by a torsional spring, where the stiffness of the torsional spring instantaneously decreases once it has exceeded a critical angle. We conducted a series of static tests to approximate model parameters. Then, we used numerical simulation to estimate the peak stresses and reaction moments experienced by the wing during a collision. We found that costal break increased the wing’s natural frequency by about 50% compared to a homogeneous wing and thus reduced the stress associated with normal flapping. Buckling did not significantly affect peak stresses during collision. Joint buckling reduced the peak reaction moment by about 32%, suggesting that the costal break enhances flight stability.

In this theoretical study, the vibration suppression and nonlinear energy transfer, as a function of a dimensionless pendulum length parameter, is investigated for an Inerter Pendulum Vibration Absorber (IPVA) attached to a linear single-degree-of-freedom spring-mass-damper system, subject to white noise excitation. Stochastic differential equations of motion are first developed and integrated to determine the evolution of the response and associated mean and mean square values for long integration times. Dynamic statistical moment equations are then developed, while arc-length continuation is used to track stationary the moments as a function of the pendulum length. Two noise intensity and damping configurations are analyzed and a critical parameter value, in both cases, is found to produce a qualitative change in the system dynamics accompanied by optimal vibration suppression. The results are compared to the response of a linear system without an IPVA to quantify the vibration suppression. Realizations in the time domain are finally calculated to provide validation for the results and gain insight into the changing dynamics of the system as a function of the pendulum length, leading to the discovery of intermittent rotation for sufficiently large pendulum length.

This paper presents the gravity balancing reliability and sensitivity analysis of robotic manipulators with uncertainties. The gravity balancing reliability of the robot is defined as the probability that the reduction torque ratio of the robot reduces below a specified threshold. This index is of great importance for assessing and guaranteeing the balancing performance of the robot in the presence of uncertainties in input parameters. In this work, the balancing design for an industrial robot using the gear-spring modules (GSMs) is proposed with the adoption of a simulation-based analysis of the gravity effect of the robot. The Monte Carlo Simulation (MCS) method with normally distributed variables (i.e., link dimensions, masses, and spring stiffness coefficients) is employed to analyze and simulate the reliability. A case study with an industrial robot is then given to illustrate the reliability performance and the sensibility of the uncertain parameters. It is found that the gravity balancing behavior is achieved even when the uncertainties are applied. The uncertainties could deteriorate the balancing performance when increasing the standard deviations by more than seven percent of their means. The dimensional parameters enjoy the most critical influence on the balancing performance.

This paper presents a nonlinear model of an inversion-based generalized cross-spring pivot (IG-CSP) using the beam constraint model (BCM), which can be employed for the geometric error analysis and the characteristic analysis of an inversion-based symmetric cross-spring pivot (IS-CSP). The load-dependent effects are classified in two ways, including structure load-dependent effects and beam load-dependent effects, where the loading positions, geometric parameters of elastic flexures, and axial forces are the main contributing factors. The closed-form load-rotation relations of an IS-CSP and a non-inversion-based symmetric cross-spring pivot (NIS-CSP) are derived with consideration of the three contributing factors for analyzing the load-dependent effects. The load-dependent effects of IS-CSP and NIS-CSP are compared when the loading position is fixed. The rotational stiffness of the IS-CSP or NIS-CSP can be designed to increase, decrease, or remain constant with axial forces, by regulating the balance between the loading positions and the geometric parameters. The closed-form solution of the center shift of an IS-CSP is derived. The effects of axial forces on the IS-CSP center shift are analyzed and compared with those of a NIS-CSP. Finally, based on the nonlinear analysis results of IS-CSP and NIS-CSP, two new compound symmetric cross-spring pivots are presented and analyzed via analytical and FEA models.

Additive manufacturing provides a rapid manufacturing method for a variety of materials with different applications. Thermoplastic Polyurethane (TPU) is a soft polymer material that can be 3D printed. In this work, we explore the mechanical properties of a 3D printed grid pattern structure with TPU. By changing the pattern’s cell size and wall thickness parameters, we control the density of the grid lattice and, as a result, the bulk elastic modulus of the structure. We compare simulation and physical compression tests and conclude that the bulk elastic modulus of a print is related to the infill percentage according to a cubic relationship, with higher infill percentage samples resulting in higher elastic moduli. The precise cell size and wall thickness parameter values are minor influences comparatively. The elastic moduli of the resulting samples span from 0.36 MPa with 23.44% infill to 21.83 MPa with 75% infill, compared to an elastic modulus of 64.31 MPa when printing at 100% density. We also explore other factors such as the sample size, the printer, the build orientation, and the sample geometry. The results have uses in a variety of applications, including a custom linear spring, a bistable gripper, or a soft robot finger.

Springs are mechanical devices that are employed to resist forces, store energy, absorb shocks, mitigate vibrations, or maintain parts contacting each other. Spring wires are commonly coiled in the forms of helixes for either extension or compression. Helical springs usually have cylindrical shapes that have constant coil diameter, constant pitch and constant spring rate. Unlike conventional cylindrical coil springs, the coil diameter of conically coiled springs is variable. They have conical or tapered shapes that have a large coil diameter at the base and a small coil diameter at the top. The variable coil diameter enables conical coil springs generate desired load deflection relationships, have high lateral stability and low buckling liability. In addition, conical compression springs can have significantly larger compression or shorter compressed height than conventional helical compression springs. The compressed height of a conical compression spring can reach its limit that is the diameter of the spring wire if it is properly synthesized. The height of an undeformed conical coil spring can have its height of its spring wire if the spring pitch is chosen to be zero. The variable coil diameter of conical coil springs provides them with unique feature, but also raises their synthesis difficulties. Synthesizing conical coil springs that require large spring compression or small deformed spring height or constant spring rate is challenging. This research is motivated by surmounting the current challenges facing conical coil springs. In this research, independent parameters are introduced to control the diameter and pitch of a conical coil spring. Different conical coil springs are modeled. Their performances are simulated using the created models. The deflection-force relationships of conical coil springs are analyzed. The results from this research provide useful guidelines for developing conical coil springs.

Toggle mechanisms are used throughout engineering to accomplish various tasks, for example residential electrical switching. The design of toggle mechanisms can be broken into three categories: determination of a topology, geometric parameterization, and optimization. While topological determination and optimization have well established processes for use in design, geometric parameterization which includes defining link lengths and spring stiffness has largely been left to engineering judgement. This paper presents a design methodology using potential energy graphs which informs the engineering decisions made in choosing mechanism parameters, giving designers higher confidence in the design. A kinematic analysis coupled with Lagrange’s equation determines the relationship between the mechanism parameters and the potential energy curve. Plotting the potential energy with respect to the generalized coordinate yields a graph with a slope that is the generalized force or moment. The relationships between parameters and their effects on the mechanism are difficult to observe in the equations of motion, but potential energy plots readily provide information pertinent to the design of toggle mechanisms and decouple their effects. The plots also allow design by position rather than time which makes the design process faster. The design process is applied to three examples: a simple toggle mechanism, a compliant mechanism, and a reconfigurable mechanism to show the nuances of the approach.

Cable-driven exoskeletons add minimal inertia and restrictions to the user’s leg while still providing feedback and quantitative measures of the user’s performance. However, cable robots require at least n + 1 cables to control n degrees-of-freedom, i.e., they require more actuators than the leg’s degrees-of-freedom, challenging their widespread adoption as wearable technology. The state-of-the-art in this field aims to reduce the number of actuated motors. In this paper, we design and evaluate a “single motor-driven” leg exoskeleton prototype based on the Cable-driven Active Leg EXoskleton (C-ALEX). The prototype consists of four crank-spring mechanisms and a crankshaft designed using epicycle analysis. The epicycle analysis is performed using discrete Fourier transform (DFT) and sine curve fitting (SCF). While DFT suggests the maximum number of epicycles to imitate the target waveform, a large number of nested epicycles is challenging to design and manufacture for implementation. To validate the epicycle-guided design, we constructed a simple crankshaft model using one epicycle. Our proposed simplified model predicted and produced the joint angles calculated from the inverse and forward kinematics of a cable-driven leg exoskeleton with multiple motors. To our knowledge, this is the first multi-cable driven exoskeleton powered by a single actuator that is designed to provide continuous assistance to the user.

By combining the reasoning design of the expert system with the analysis and calculation of spring based on a mathematical model and its optimal design, an intelligent spring CAD system has been established. The expert system technique is adopted for such non-calculating designing steps as the selection of scheme, the determination of parameters as well as for the development of the technological process, thus greatly strengthening the original CAD system of springs. This paper provides a detailed description of the function, structure, characteristic features and significance of the said system.

Linkages are inherently light, inexpensive, strong, adaptable to high speeds and have little friction. Moreover the class of functions suitable for linkage representation is large. For all these reasons numerous recent works deal with the problem of design mechanisms for robotic applications, but very often in terms of components such as gripper, transmission, balancing. We investigate a new application for linkages, using them to design industrial manipulator. The selected mechanism for this application is a four bar linkage with an adjustable lengh for exact path generation. This adjustment is performed by a track or cam which is substituted to a bar. By this mean, we define a cam-modulated linkage which possess superior accuracy potential and is capable of accomodating of industrial design restrictions. Such a kinematic chain is free from structural error for path generation and the presence of the track introduces the flexibility and versality in the usefull four bar chain. The synthesis technique of cam modulated linkage utilizes loop closure equations, envelop theory to find the centerline and the profile of the track. These techniques provide a systematic approach to the design of mechanism for path generation when extreme accuracy is required. In order to complete an contribution, we take in consideration the static balancing of the synthesized manipulator. To achieve static mass balancing we use the potential energy storage capabilities of linear springs, and integrated it with the non-linear motion of mechanism to provide an exact value of the desired counter loading functions. Examples are worked to demonstrate applications of these procedures and to illustrate the industrial potential of spring balancing and cam-modulated linkage.

We report on using problem partitioning and constraint-guided search as a generalized approach to problem-solving in preliminary design. Specifically, a generic design template has been created as a tool to structure information to facilitate problem-solving in three different domains. The approach has been tested through the implementation of knowledge-based systems for the preliminary design of mechanical springs, composite sublaminates and expert systems. Information in each implementation has been partitioned as hierarchical levels of abstraction related through constraints. Function identifies the top level design goals to reduce the search involved for feasible solutions. Goal-directed search, driven by the design application and top-down refinement, reduces the number of possible alternatives. The commonalities extant in the domains have been represented as design goals at three levels of abstraction in the design template. Similar frame-based knowledge representations with inheritance hierarchies and mixed reasoning have been developed for the KEE™-based implementations in each domain. Distinctions among the domains have been modelled as low level slots in the frame hierarchy. Parametric studies in the domains of mechanical springs, composite sublaminates and expert systems indicate that the minimum number of decision levels required to characterize the preliminary design process in these domains is three; fewer levels would be insufficient to fundamentally characterize the designs. Further, it is observed hierarchical structuring of design information facilitates capturing the interactions among design variables at different levels of abstraction. By using the template representation and reasoning in other divisible domains, the effectiveness of our approach can be further investigated.

A two-degree-of-freedom (2-DOF), analytical model of a hydraulic valve lifter is derived. Special features of the model include the effects of bulk oil compressibility, multi-mode behavior due to plunger check valve modeling, and provision for the inclusion of third and fourth body displacements to aid In the use of the model in extended, multi-DOF systems. It is shown that motion of the lifter plunger and body must satisfy a coupled system of third-order, non-linear differential equations of motion. It is also shown that the special cases of zero oil compressibility and/or 1-DOF motion of lifter plunger can be obtained from the general third-order equations. For the case of zero oil compressibility, using Newtonian fluid assumptions, the equations of motion are shown to reduce to a system of second-order, linear differential equations. The differential equations are numerically integrated in five scenarios designed to test various aspects of the model. A modal analysis of the 2-DOF, compressible model with an external contact spring is performed and is shown to be in excellent agreement with simulation results.