In a planetary gear train (PGT), the power loss by tooth friction is a function of the potential power developed within the gear train elements rather than that being transmitted through it. In the present work, we focus on the operating conditions of two-degree-of-freedom (two-DOF) PGTs. Any operating condition induces its own internal power flow pattern; this implies that tooth friction loss depends on the mechanism of power loss developed in the gearing that differs from one case to another over the entire range of operating conditions. The approach adopted in this paper stems from a unification of the kinematics and tooth friction losses of PGTs and is based on potential powers and power ratios. The range of applicability of the power relations is investigated and clearly defined, and tooth friction loss formulas obtained by their use are tabulated. A short comparison with formulas currently available in the literature is also made. The simplicity of the proposed method for analyzing two-input or two-output planetary gear trains is helpful in the design, optimization, and control of hybrid transmissions. It assists particularly in choosing correctly the appropriate operating conditions to the involved application.

In this technical brief, the authors compare the torque capacity of a magnetorheological (MR) fluid brake with a conventional frictional disk brake. In the development of the torque models for both brakes, a mathematical expression for the compared torque ratio is presented. For the frictional disk brake, constant pressure and constant wear theories are considered, while static torque of the MR fluid brake is considered for comparison purpose only. Throughout the analysis, the outer radius of the compared brakes is assumed to be the same to ensure similarity of size, while the inner radius is selected to achieve maximum values of braking torque for both brake designs. Reasonable values of design variables for each brake are obtained from references and adopted in this study for making comparisons between the two designs. In conclusion, it is shown that the torque capacity for a frictional disk brake is 10–18 times greater than the torque capacity for a MR fluid brake of similar size.

Origami is traditionally implemented in paper, which is a passive material. This research explores the use of material with embedded electronics such as printed circuit boards (PCB) as the medium for origami folding to create an interactive folding experience and to generate foldable objects with added functionalities. PCBs are produced as 2D shapes. By folding PCB arrays, it is possible to create 3D objects that contain electronic functions. Conductivity, output devices (such as light emitting diodes) and microcontroller computation can create an interactive folding experience, for user guidance and verification of the folding. We call this approach and methodology PCB origami. The work presented in this paper describes two unique interaction and fabrication techniques for creating and folding electronic materials. We demonstrate prototypes and present verification/evaluation strategies for guiding the user through the folding process.

This paper investigates the geometry of a foldable barrel vault with modified Miura-ori patterns, which displays a curvature during the motion. The principal of spherical trigonometry was used to obtain the relationship of the inclined angles between adjacent folded papers of Miura-ori. Then, the radius, span, rise, and longitudinal length of the foldable barrel vault in all configurations throughout the motion are determined. The results show that the radius of curvature grows exponentially and the span increases during deployment. Furthermore, the rise increases first, followed by a decrease with increasing deployment angle.

In this study, we present an analytical approach for synthesizing line actuation spaces of a parallel flexure mechanism (PFM) that can help designers to arrange linear actuators within the PFM in a correct and optimal way. On the basis of screw theory and upon an assumption of small deformations, an important synthesis criterion stated as “any actuation space of a flexure mechanism is always linearly independent of its constraint space” has been derived and disclosed for the first time. Guided by this criterion, a general synthesis process for the line actuation spaces of PFMs is introduced and demonstrated with several selective examples. The proposed synthesis criterion and process will enable designers to (i) systematically formulate line actuation spaces in the format of screw systems; (ii) likely yield a multiple solution to actuation spaces; and (iii) potentially determine an optimal result from those alternatives for actuator placement.

The present research focuses on the development of a multifunctional wheel-embedded assembly for electrically powered vehicles. It must perform the core functions of a road-going vehicle—propulsion, braking, steering, and suspension—with all functional mechanical elements within the wheel envelope. The originality of the research lies in the integration of all aforementioned functions at once. The proposed concept exhibits two off-center electric motors, sliding pillar-type suspension with direct-drive steering at the top, and braking is achieved by means of a conventional disk and caliper assembly, but servohydraulically actuated with magnetically actuated parking brake. It makes extensive use of geometric nesting and function sharing—the large transmission gear doubles as hub and wheel carrier, the suspension pillar is also used for steering torque transmission. Finally, the advantages and disadvantages of the proposed concept are addressed, as well as practical applications.

In the textbook by Wahl (1963, Mechanical Springs, 2nd ed., McGraw-Hill, New York, Chap. 20), he derived an equation predicting the diametral growth of a helical spring as the spring is compressed from free to solid height, and the spring's ends are free to rotate. A recent comparison with test data for growth of compression springs revealed that the calculated growth predicted by the Wahl formula did not agree well with measured values. Review of the Wahl derivation uncovered an arithmetic error that, when corrected, brought the calculated and measured diameters into closer agreement. The corrected diametral growth equation presented herein bounds the original data provided by Wahl, better matches an alternate growth equation derived by Ancker and Goodier for most springs evaluated, predicts larger growth than the original Wahl equation, and is a better fit to recent measured data.

Analytical target cascading (ATC), a hierarchical, multilevel, multidisciplinary coordination method, has proven to be an effective decomposition approach for large-scale engineering optimization problems. In recent years, augmented Lagrangian relaxation methods have received renewed interest as dual update methods for solving ATC decomposed problems. These problems can be solved using the subgradient optimization algorithm, the application of which includes three schemes for updating dual variables. To address the convergence efficiency disadvantages of the existing dual update schemes, this paper investigates two new schemes, the linear and the proximal cutting plane methods, which are implemented in conjunction with augmented Lagrangian coordination for ATC-decomposed problems. Three nonconvex nonlinear example problems are used to show that these two cutting plane methods can significantly reduce the number of iterations and the number of function evaluations when compared to the traditional subgradient update methods. In addition, these methods are also compared to the method of multipliers and its variants, showing similar performance.

Gears and gear systems, like any other mechanical system, are subjected to design parameter, and loading uncertainties emanating from inherent randomness, manufacturing, and assembly errors. The traditional deterministic approach to the design of such systems overlooks these uncertainties. This work presents a novel probabilistic multibody dynamic analysis (PMBDA) that enhances the deterministic design practice of gears and gear systems. A contact based, rigid multibody spur gear pair model with random loading, and design parameters has been developed. An advanced mean based on fast probability integration method was implemented to perform a reliability analysis of performance measurements: dynamic factor, root bending stress, and fatigue life of gears. Probabilistic sensitivity analysis of these performance functions to several random variables was also determined. In addition to revealing system reliability or probability of failure, the PMBDA approach also helps designers to consider certain variables critically.

Parallel manipulators possess several advantages compared to serial robots, including the possibilities for high acceleration and high accuracy positioning of the manipulated platform. However, the majority of all proposed parallel mechanisms suffer from the combined drawbacks of a small positional workspace in relation to the manipulator footprint and a limited range of rotations of the manipulated platform. This paper analyses a recently proposed six-degrees-of-freedom parallel mechanism that aims to address both these issues while maintaining the traditional advantages of a parallel mechanism. The investigated manipulator consists of six actuated coaxial upper arms that are allowed to rotate indefinitely around a central cylindrical base column and a manipulated platform where five of the six joint positions are collinear. The axis-symmetric arm system leads to an extensive positional workspace while the proposed link arrangement increases the range of achievable platform rotations. The manipulator workspace is analyzed in detail and two methods to further increase the rotational workspace are presented. It is shown that the proposed manipulator has the possibility of a nonsingular transition of assembly modes, which extends the usable workspace. Furthermore, it is demonstrated how an additional kinematic chain can be utilized to achieve infinite platform rotation around one platform axis. By introducing additional mobility in the manipulated platform, a redundantly actuated mechanism is avoided.

Most research papers that exploit conical springs focus only on conical springs with a constant pitch. In order to increase the range of possibilities for designers, this paper proposes a study of conical springs with other types of spirals projected on the conical shape. This study is related to three other types of conical springs: with a constant helix angle, with a constant stress at solid and with a fully linear load-length relation. For each spring, we give the equation of the spiral, the formula of the initial stiffness, and formulae to calculate the nonlinear part of the load-length relation for fully telescoping springs. We also report an experimental study performed to analyze the accuracy of the proposed study based on springs made by fused deposition modeling.

Smart valves are used in cooling applications and are responsible for regulating and supplying the coolant, which is critical for safe and effective operation of many components on naval and commercial ships. In order to be operated under local power (for various mission-critical reasons) they need to consume as little energy as possible in order to ensure continued operability. This paper focuses on optimized design of a typical system using high fidelity nonlinear dynamic models for all the subsystems with full consideration of stability constraints. A simulated annealing algorithm is applied to explore optimal design using two sets of design variables. The results indicate that substantial amount of energy can be saved by an intelligent design that helps select parameters carefully, but also uses hydrodynamic loads to augment the closing effort.

The purpose of this study is to investigate the effect of driving method and crank arrangements on the performance of a reconstructed ancient Chinese wooden horse carriage. The results demonstrate better transmission efficiency when the driving torque of wooden horse carriage acts on the crank shaft. The analysis of crank arrangements shows that the phase angle between front and rear legs on the same side should be 0 deg or 90 deg and the one between the legs on the different sides should be 180 deg. These results are beneficial to the future reconstruction of the ancient Chinese wooden horse carriage.

Kriging is used extensively as a metamodel in multidisciplinary design optimization. The correlation matrix used in Kriging metamodeling frequently becomes ill-conditioned. Therefore different numerical methods used to solve the Kriging equations affect the search for the optimum Kriging parameters and the ability of the Kriging surface to accurately interpolate known data points. We illustrate this by firstly computing the inverse of the correlation matrix in the Kriging equations, and secondly by solving the systems of equations using decomposition and back substitution, thereby avoiding the inversion of the correlation matrix. Our results clearly show that by decomposing and back substituting, the interpolation accuracy is maintained for significantly higher condition numbers. We then show that computing the natural logarithm of the determinant using additive calculations as opposed to multiplicative calculations significantly reduces numerical underflow errors encountered when searching for the optimum Kriging parameters. Although the effect of decomposition and back substitution are known, and the underflow difficulties when computing the natural logarithm of the determinant of the correlation matrix has been mentioned in passing in Kriging literature, this work clearly quantifies and reinforces these methods, hopefully for the benefit of researchers entering the field.

In the design of wind turbine gearboxes, the most important objective is to improve the durability to guarantee a service life of more than 20 years. This work investigates how external loads caused by wind fluctuation influence both the load distribution over the gear tooth flank and the planet load sharing. A whole system model is developed to analyze a wind turbine gearbox (WTG) that consists of planetary gearsets. Two models for different design loads are employed to quantify how external loads acting on the input shaft of the WTG affect the load distribution of the gears and the load sharing among the planets under quasi-static conditions. One model considers only the torque for the design load, whereas the other model also considers non-torque loads. For two models, the results for the gear mesh misalignment, contact pattern, load distribution, and load sharing are different, and this leads to different gear safety factors. Therefore, the results indicate that it is appropriate to consider the non-torque loads in addition to the torque as the design load for a WTG, and that this is very important to accurately determine the design load that guarantee the service life of a WTG.

Straight bevel gears are widely used in the plant of large-sized power generation when the gears have large size. The purpose of this study is to manufacture the large-sized straight bevel gears with equi-depth teeth on a multitasking machine. The manufacturing method has the advantages of arbitrary modification of the tooth surface and machining of the part without the tooth surface. For this study, first, the mathematical model of straight bevel gears by complementary crown gears considering manufacture on multitasking machine is proposed, and the tooth contact pattern and transmission errors of these straight bevel gears with modified tooth surfaces are analyzed in order to clarify the meshing and contact of these gears. Next, the numerical coordinates on the tooth surfaces of the bevel gears are calculated and the tooth profiles are modeled using a 3D-Computer-Aided Design (CAD) system. Five-axis control machines were utilized. The gear-work was machined by a swarf cutting using a coated carbide end mill. After rough cutting, the gear-work was heat-treated, and it was finished based on a Computer-Aided Manufacturing (CAM) process through the calculated numerical coordinates. The pinion was also machined similarly. The real tooth surfaces were measured using a coordinate measuring machine and the tooth flank form errors were detected using the measured coordinates. As a result, the obtained tooth flank form errors were small. In addition, the tooth contact pattern of the manufactured large-sized straight bevel gears was compared with those of tooth contact analysis. The data showed good agreement.

A type of modified-hourglass worm gear drive, frequently called type-II worm gearing for short, has various favorable meshing features. Its sole shortcoming is the undercutting of the worm wheel. By adopting a slight modification, this problem can be overcome due to the removal of a part of one subconjugate area containing the curvature interference limit line. To measure how effectively the undercutting is avoided, a strategy to determine the meshing point in the most severe condition is proposed for a type-II worm drive. The strategy presented consists of two steps. The first step is to establish a system of nonlinear equations in five variables in accordance with the theory of gearing. The second step is to solve the system of nonlinear equations by a numerical iteration method to ascertain the meshing point required. A numerical example is presented to verify the validity and feasibility of the proposed scheme.

This work focuses on the design, development, and testing of an inexpensive, low-profile, cartwheel flexure mechanism for torque measurement. It has been designed primarily for use in a rehabilitation and diagnostics instrument for the treatment of ankle injuries. The sensor is manufactured rapidly and at low-cost using an Omax™ abrasive waterjet machine. Strain gauges are bonded to the flexure beams to measure applied strain using a full wheatstone bridge circuit. Displacement, force, and torque are then calculated from the measured circuit voltage; power and velocity can also be determined if required by the application. Experimental results show that there exists a linear relationship between applied torque and output voltage of the wheatstone bridge for the nested cartwheel flexure design. Furthermore, results of preliminary tests of an ankle rehabilitation device show that it fulfills a need not currently satisfied by current rehabilitation and diagnostic technology in physical medicine and rehabilitation.

Iterative algorithms are widely applied in reliability analysis and design optimization. Nevertheless, phenomena of failed convergence, such as periodic oscillation, bifurcation, and chaos, are oftentimes observed in iterative procedures of solving some nonlinear problems. In the present paper, the essential causes of numerical instabilities including periodic oscillation and chaos of iterative solutions are revealed by the eigenvalue-based stability analysis of iterative schemes. To understand and control these instabilities, the stability transformation method (STM), which is capable of tackling numerical instabilities of iterative algorithms in reliability analysis and design optimization, is proposed. Finally, several benchmark examples of convergence control of PMA (performance measure approach) for probabilistic analysis and the SORA (sequential optimization and reliability assessment) for reliability-based design optimization (RBDO) are presented. The observations from the benchmark examples indicate that the STM is a promising approach to achieve convergence control for iterative algorithms in reliability analysis and design optimization.

When magnetic resonance (MR) images are collected while applying a load to the knee joint, additional information about the joint response to loading can be acquired such as cartilage deformation, whole joint and ligament stiffness, or physiological estimates of weight-bearing joint positions. To allow load application and controlled lower limb movement in supine MR imaging, the knee loading apparatus (KLA) was designed to apply safe and physiologically relevant controlled loads to the knee joint, position the knee through a range of flexion angles, and operate successfully in a magnetic environment. The KLA is composed of three main components: a remotely operated custom hydraulic loading system, a logic system that interfaces with the user, and modular non ferromagnetic positioning frames. Three positioning frames are presented for application to anterior tibial loading, tibiofemoral compression, and patellofemoral compression at multiple knee flexion angles. This system design makes improvements over current devices. Safe remotely applied loads (hydraulic loading system) can be applied by either subject or tester and in multiple locations simultaneously. Additionally, loads can be altered at any time in a continuous manner without electrical interference. Transportability was improved due to a smaller footprint. The KLA has the flexibility to attach any positioning frame with many possible loading scenarios without changing the loading mechanism or logic systems, and allows force values over time to be output rather than estimated. An evaluation of the load repeatability (within 7% of applied load) and accuracy (0.5–14.9%) demonstrates the feasibility of this design for investigations into in vivo knee joint responses to loading.