Planar Mechanisms Research Articles

FUNCTION GENERATION OF A WATT II TYPE PLANAR MECHANISM WITH PRISMATIC OUTPUT USING DECOMPOSITION AND CORRECTION METHOD

The method of decomposition is a useful method for function generation with multi-loop mechanisms. The recently introduced correction methods applied together with the method of decomposition allows the designer to cancel out the errors in the first loop of a two-loop mechanism with the errors in the second loop. In this study, the decomposition and correction method is applied for a Watt II type planar six-link mechanism with prismatic output. Five design parameters are defined for each loop resulting in ten design parameters in total. The design parameters are determined analytically. The generation error is decreased by adjusting free parameters such as the limits of the some joint angles and parameters due to the decomposition of the function to be generated, while considering several constraints such as link lengths ratios and ranges of the joint variables. The success of the method is illustrated with a numerical example.

Nine-parameter path synthesis of planar four-bar mechanism with the aid of the general equation of coupler curve

The design of a four-bar mechanism to generate a prescribed path with minimal error is possible by using the maximum number of parameters that are effective in the path synthesis of the mechanism. In this study, the design of four-bar mechanisms, which intersect the given path curve at nine points, was dealt with in two stages. In the first step, the kinematic equations of the mechanism were used to implement the preliminary design based on the five parameters and closed-form solving. Thus, all the possible solution values have been reached with five parameters. In the second stage, which is the final design, the general algebraic form of coupler curve, which is dependent on the nine dimensions of the mechanism and of the sixth order, was obtained. An objective function de-rived from the obtained equation is subjected to an optimization process with nine-parameters by using the dimensions obtained from the preliminary design as an initial value, and the error between the actual and the desired path is minimized. The efficiency of the method is shown by numerical example made by choosing difficult paths to produce four-bar mechanisms.

Optimal synthesis of a planar mechanism using Matlab: Example of slider crank in a rowing motion

<abstract> <p>This paper illustrates the conducted effort to introduce the methodology of optimal synthesis of mechanisms through an engineering problem under Matlab. This project is part of a first course on poly-articulated mechanisms and robotics at the graduate level. The course combines both the theoretical and implementation under Matlab aspects to achieve its goals. The example of the rowing machine is considered to introduce the crank-slider mechanism and the kinematic analysis using complex numbers. The mechanism is associated with a spring to ensure the device simulating the resistance in the rowing bench simulator. The optimal synthesis problem is formulated for the desired effort to perform and solved using the Sequential Quadratic Programming method. All developments are implemented under Matlab.</p> </abstract>

Maneuverability prediction of the wave glider considering ocean currents

The wave glider powered by waves has a unique dual-body architecture and can perform long-duration operational tasks in the ocean. In this paper, to accurately predict its maneuverability, the horizontal plane 3-degree of freedom (DOF) dynamic models of the surface float and the submerged glider are established separately. The influence of ocean currents is considered, and the influence of the torsional moment of the umbilical cable is considered for the first time. The hydrodynamic coefficients of the submerged glider will vary with different rudder angles and angles of attack of incoming flow. The computational fluid dynamics (CFD) method is used to analyze and calculate added mass coefficients and damping coefficients corresponding to different rudder angles based on planar motion mechanism (PMM) test simulation and oblique navigation dynamic test simulation. The flow fields are analyzed under different working conditions. The structural parameters of the wave glider and the hydrodynamic coefficients obtained from the simulation are brought into the dynamic model. The rotary motion and the Z-shaped motion under different sea conditions and currents are numerically analyzed. The difference of the hysteresis of the surface float relative to the submerged glider in yaw motion are analyzed under different ocean currents and rudder angles. Sea trial and simulation results show that the established dynamic model and obtained hydrodynamic parameters can accurately basically predict the maneuvering performance of the wave glider.

Analysis and design method of a class of reconfigurable parallel mechanisms by using reconfigurable platform

This paper proposes a method to design reconfigurable parallel mechanisms by applying reconfigurable platforms. According to the requirements of convenience and reliability, the basic rules for designing a reconfigurable platform are proposed. Based on a planar four-bar mechanism, single- and double-stage mechanisms are designed based on DOF (Degree of Freedom) formulation, and the single- and multi-loop reconfigurable platforms are both presented. For the spatial reconfigurable platform, the F1 (one independent force), C1 (one independent couple), F2C1 (two independent forces and one independent couple), and F1C2 (one independent force and two independent couples) over-constrained mechanisms are designed according to screw theory. To meet the multi-limb, parallel-mechanism structural requirement, single-loop over-constrained mechanisms are developed to multi-loop over-constrained mechanisms. Finally, a typical reconfigurable parallel mechanism is selected. Both the kinematics and performance analysis are investigated, and dimension synthesis based on multi-objective optimization is explored using some global indices.

Design of off-axis reflective optical system based on planar linkage mechanism

In this paper, we propose a straightforward and dynamic approach to design unobstructed off-axis reflective image systems using a planar linkage mechanism. Objective: The advantage of this design is that it simplifies the process of modeling and optimizing the optical system. Method: The center of the surface is placed at the hinge point, and its tilt angle and position are determined by the adjacent hinge coordinates, and then the curvature of each reflector is determined by the relationship of the optical power. Result: In order to verify the feasibility and convenience of the method, an off-axis four-mirror free-form system is designed, with field of view of 5° × 5°, and the results of the optimized system show that the MTFs greater than 0.8 at 30 lp /mm.

Input coupling modeling method for a three-PRR flexure-based compliant stage

This paper presents the input coupling modeling method for a three-PRR flexure-based compliant stage. The input coupling modeling for planar compliant mechanisms is first established. The kinematic structure of a three-PRR compliant stage is then designed, and its input coupling is derived by using the proposed method. Subsequently, the validation and analysis are carried out by using finite element method (FEM). The relationships between two main parameters and the input coupling rate of the three-PRR compliant stage are discussed, and the decoupling region is then determined. Finally, its geometrical parameters are optimized, and the workspace calculated by the analytical method is compared with that obtained from FEM. It not only provides a new input coupling modeling method for flexure-based compliant mechanisms, but also provides a reference for the design of three-PRR mechanisms.

CALIBRATION OF THE ROBOTIC ARM WITH CORRECTIONS USING LOCAL LINEAR NEURO-FUZZY MODELS

The paper deals with the enhancement of the robotic arm calibration using corrections based on local linear neuro-fuzzy models. After the standard calibration of the geometric parameters in the robot's kinematic model, there are still residual errors between the measured positions and the positions predicted by the model. The source of these errors are various non-geometric parameters and nonlinear phenomena that traditional kinematic calibration models do not include. The neuro-fuzzy model based on a locally linear model tree can approximate the residual error as a function of the robot's joint angles. Adding this approximation to the output of the calibrated robot model significantly increases the accuracy of the endeffector position. The results of the described method were verified and compared with other approaches on a simulation model of a flexible planar two-link mechanism. Experimental verification was performed on an industrial robot Stäubli TX200 with data measured by Leica laser tracking device.

Direct Kinetostatic Analysis of a Gripper with Curved Flexures.

Micro-electro-mechanical-systems (MEMS) extensively employed planar mechanisms with elastic curved beams. However, using a curved circular beam as a flexure hinge, in most cases, needs a more sophisticated kinetostatic model than the conventional planar flexures. An elastic curved beam generally allows its outer sections to experience full plane mobility with three degrees of freedom, making complex non-linear models necessary to predict their behavior. This paper describes the direct kinetostatic analysis of a planar gripper with an elastic curved beam is described and then solved by calculating the tangent stiffness matrix in closed form. Two simplified models and different contributions to derive their tangent stiffness matrices are considered. Then, the Newton-Raphson iterative method solves the non-linear direct kinetostatic problem. The technique, which appears particularly useful for real-time applications, is finally applied to a case study consisting of a four-bar linkage gripper with elastic curved beam joints that can be used in real-time grasping operations at the microscale.

An analytical game-based design of crank-rocker mechanisms with optimum stroke, time ratio and transmission angle

In this study, an analytical approach based on bi-level multi-objective game theory is proposed and implemented for dimensional synthesis of the planar crank-rocker four-bar mechanisms. Two players, namely, Stroke ([Formula: see text]) and Time Ratio ([Formula: see text]) are considered in the level playing the role of a leader. The third player, Transmission Angle ([Formula: see text]), is placed in a lower level operating with the role of the follower’ role. Players’ behavior at upper level is also modeled as a cooperative game. In addition to this, the interaction between upper and lower levels is modeled as a Stackelberg game wherein an analytical approach is given to provide an explicit function of the follower’s Rational Reaction Set (RRS). Such analytical approach of Stackelberg game theory leads to an interesting relationship of length of the coupler and rocker links. It is, therefore, advised that by adopting equal lengths for coupler link and rocker link, one can guaranty the optimality of the transmission angle deviation, ensuring the Grashof condition. Consequently, the stroke, time ratio, and transmission angle criteria are derived explicitly as mathematical functions explaining the links of mechanism’s normalized dimensions. The aforementioned approach coupled with the proposed formulas and charts, greatly simplifies the synthesis of the mechanisms with optimal transmission angle while adopting any desired values of both stroke and time ratio. The theoretical approach proposed are explained with illustrated examples.

Simulation of Turning Manoeuvre of Planing Craft Taking Into Account the Running Attitude Change in a Simplified Manner

Abstract The modelling and simulation of planing craft manoeuvres requires coupled six degrees of freedom (6 DOF) motion equations. A coupled 6 DOF motion equation needs hundreds of manoeuvring hydrodynamic coefficients (MHCs) that are mostly determined using the planar motion mechanism (PMM) test. The number of test runs is too high, unless a kind of simplification is imposed to the motion equations. This study modifies 6 DOF motion equations to 4+2 DOF motion equations in which heave and pitch equations are replaced by dynamic draught and trim (so-called running attitude), respectively. The method is applicable for a manoeuvre that commences in the planing regime and ends in the same regime. On that basis, the PMM test is conducted and the model is restrained in the vertical plane at a certain running attitude, determined by a resistance test. The 4+2 DOF method, together with MHCs from the PMM test, are employed for the simulation of turning manoeuvres of a 25° prismatic planing hull. The results of the simulation indicate that the 4+2 DOF method reasonably predicts the path of the craft during the turning manoeuvre and cuts the number of PMM tests required at the same time. The PMM test results show that MHCs are highly related to forward speed and wetted surfaces. The turning manoeuvre simulation shows that the non-linear terms of MHCs cannot be ignored. The STD/L (Steady Turning Diameter divided by Length of the craft) for a planing craft is very large, compared to ships.

Unveiling the planar deformation mechanisms for improved formability in pre-twinned AZ31 Mg alloy sheet at warm temperature

To investigate the role of pre-twins in Mg alloy sheets during warm planar deformation, the stretch forming is conducted at 200 °C. Results suggest the formability of the pre-twinned AZ31 Mg alloy sheet is enhanced to 11.30 mm. The mechanisms for the improved formability and the deformation behaviors during the planar stretch forming are systematically investigated based on the planar stress states. The Schmid factor for deformation mechanisms are calculated, the results reveal that planar stress states extremely affect the Schmid factor for {10-12} twinning. The detwinning is activated and the prismatic slip is enhanced in the pre-twinned sheet, especially under the planar extension stress state in the outer region. Consequently, the thickness-direction strain is accommodated better. The dynamic recrystallization (DRX) type is continuous DRX (CDRX) regardless of the planar stress state. However, the CDRX degree is greater under the planar extension stress state. Some twin lattices deviate from the perfect {10-12} twinning relation due to the planar compression stress state and the CDRX. The basal texture is weakened when the planar stress state tends to change the texture components.

Perturb and optimize users’ location privacy using geo-indistinguishability and location semantics

Location-based services (LBS) are capable of providing location-based information retrieval, traffic navigation, entertainment services, emergency rescues, and several similar services primarily on the premise of the geographic location of users or mobile devices. However, in the process of introducing a new user experience, it is also easy to expose users’ specific location which can result in more private information leakage. Hence, the protection of location privacy remains one of the critical issues of the location-based services. Moreover, the areas where humans work and live have different location semantics and sensitivities according to their different social functions. Although the privacy protection of a user’s real location can be achieved by the perturbation algorithm, the attackers may employ the semantics information of the perturbed location to infer a user’s real location semantics in an attempt to spy on a user’s privacy to certain extent. In order to mitigate the above semantics inference attack, and further improve the quality of the location-based services, this paper hereby proposes a user side location perturbation and optimization algorithm based on geo-indistinguishability and location semantics. The perturbation area satisfying geo-indistinguishability is thus generated according to the planar Laplace mechanism and optimized by combining the semantics information and time characteristics of the location. The optimum perturbed location that is able to satisfy the minimum loss of location-based service quality is selected via a linear programming method, and can be employed to replace the real location of the user so as to prevent the leakage of the privacy. Experimental comparison of the actual road network and location semantics dataset manifests that the proposed method reduces approximately 37% perturbation distance in contrast to the other state-of-the-art methods, maintains considerably lower similarity of location semantics, and improves region counting query accuracy by a margin of around 40%.

Type synthesis of reconfigurable single-loop mechanisms based on planar rhombus mechanisms

This paper deals with the type synthesis of reconfigurable single-loop mechanisms (RSLMs) using screw theory. A novel approach is proposed to synthesize RSLMs by inserting two or four revolute joints to a planar rhombus 4R mechanism. Using the proposed approach, four types of wrench systems of RSLMs are obtained. The reconfiguration analysis of an RSLM with a constraint force system is then carried out using the kinematics close-loop equation and screw theory method. By locking the R joints, it can be found that the mechanism can realize a 1-DOF planar 4R mode, a 1-DOF Bricard mode, a 2-DOF serial mode, a 1-DOF coaxial mode, a 1-DOF Bennett mode, and a 2-DOF spatial 8R mode. Furthermore, four transition configurations among different modes are identified. To verify motion modes of the mechanisms, serval 3D printed models are also presented. This work provides a framework for further study of type synthesis reconfigurable mechanisms from overconstrained single-loop mechanisms.

Optimization with Genetic Algorithm (GA): Planar Mechanism Synthesis

Optimization with Genetic Algorithm (GA): Planar Mechanism Synthesis

DLPM: A dynamic location protection mechanism supporting continuous queries

SummaryCurrently, the protection of users' location privacy, particularly for moveable users, is a major concern for both academia and business. In order to receive required services, a moveable user needs to constantly disclose his/her location information with an untrusted third party in his/her locations, which raises security and privacy issues. To settle the above problems, in this work, we creatively integrate local differential privacy (LDP) with conditional random field (CRF) to facilitate continuous location sharing among moveable users. Firstly, we advance a novel approach of employing CRF to represent users' mobility. After that, we establish a system to provide continuous location sharing by combining the ‐location set and ‐LDP. Finally, we evaluate the system performance on actual data sets. The experimental results indicate that our technique outperforms the planar isotropic mechanism (PIM) and AGENT.

The Manufacture of Curved Crease Surfaces Starting from Kinematic Analysis of Planar Mechanisms

Achieving curved crease surfaces is a current challenge for designers, the field still underexplored. The curve on which the bending is performed can present extremely complicated shapes that must be accurately generated through various technological processes. For this aim, a planar mechanism consisting of an ellipsograph, a conchoidograph and an RRR dyad—whose inner joint generates the targeted connecting rod curve—was proposed in this paper. Parametrizing the lengths of the elements of the RRR dyad, the correlation coefficient of the rotations of the leading elements and the directions of these movements result in different connecting rod curves, which can be used to obtain the folded surfaces; the optimization, according to various criteria, will be explored for the automatic generation of some design solutions. With the help of the Altair program, for some given geometrical data of the mechanism, both the drawing of the curve on plates of different initial shapes and the simulation of their folding by applying compression forces on the bounding surfaces were carried out. By cutting the deformed shape, folded surface units used in tessellations are obtained.

Dynamic response and dynamic accuracy reliability of planar mechanism with multiple lubricated clearances

Dynamic response and dynamic accuracy reliability of planar mechanism with multiple lubricated clearances

Dynamic analysis of a three-fingered deployable metamorphic robotic grasper

This paper selects a three-fingered deployable metamorphic robotic grasper as the studied object and presents a distributed dynamic modeling method for the multi-body system based on the metamorphic mechanism. Considering that the grasper contains two independent motion configurations, dynamic models of them are independently established, and then the final dynamic model of the whole grasper is formed. To further improve the modeling accuracy, it is creatively proposed that irregular links can be seen as rigid connections of multiple regular links, by which the dynamic model for the deployment motion of the grasper is firstly established via the Lagrange equation. For the grasping motion, since the finger of the grasper can be equivalent to a planar 4R serial mechanism, the dynamic models of the base mechanism and the basic module are established by the Lagrange equation to obtain the relationships between the driving forces and the equivalent torques. The whole grasper is then established by the recursive Newton-Euler method to enhance the modeling efficiency. Finally, the effectiveness of the dynamic model is well verified by the dynamic simulation.

Computer-aided synthesis of planar mechanisms with one multiple-joint

• An isomorphism identification algorithm is presented for multiple-joint mechanisms. • A method for synthesizing planar mechanisms with one multiple-joint is proposed. • The database of planar multiple-joint mechanisms with up to 16 links is created. In the innovative design for mechanism-based devices and robots, it is crucial to synthesize as many diverse kinematic structures of available mechanisms as possible. Despite the widespread applications of multiple-joint mechanisms in various mechanical systems, few contemporary approaches concentrated on the synthesis of multiple-joint mechanisms. Herein, a computer-aided method is presented to synthesize all feasible non-isomorphic mechanisms with one multiple-joint. First, tricolor topological graphs are introduced that denote the structures of multiple-joint mechanisms. Second, two vertex classification methods are proposed, based on the calculations for the distance and vertex degree, to reduce the number of times required for the isomorphism identification of the generated tricolor topological graphs. Third, an approach is presented to automatically eliminate isomorphic tricolor topological graphs whose fixed vertices exist in the same advance vertex group. Then, a computer-aided method is proposed for synthesizing the tricolor topological graphs of planar mechanisms with one multiple-joint. Finally, a database of synthesized multiple-joint mechanisms with up to 16 links and 11 degrees of freedom (DOFs) is created, and the synthesis results are compared and discussed.