Planar Four-bar Mechanism Research Articles

Dimensional synthesis of motion generation of a planar four-bar mechanism

A motion generation method for a planar four-bar mechanism without prescribed timing is proposed in this article. A characteristic of coupler points is found: for the coupler points of a four-bar mechanism in a standard installation position rotated by the corresponding input angle clockwise around the origin of the Cartesian coordinate system xOy, the generated points lie on the feature coupler circles. Next, based on this, the design process is divided into three steps. In the first step, the relative input angles, the relative coupler angles and five geometric parameters of the desired four-bar mechanism are optimized. In the second step, the basic dimensional types and initial input angle are determined, and then, the input angles are obtained. In the third step, the real size of the desired linkage mechanism is calculated. Because the dimension of the design variables in each step is exceptionally small, the motion synthesis method can yield design solutions with high precision in a short time. Six comparison examples are presented to demonstrate the efficacy of the proposed method. In addition, the method is used to design a robot for lower limb rehabilitation for application to the human foot.

Dynamic analysis of planar four-bar mechanism with clearance in microgravity environment

Dynamic analysis of planar four-bar mechanism with clearance in microgravity environment

Function generation with planar four-bar mechanisms as a mixed problem of correlation of crank angles and dead center design

Function generation with planar four-bar mechanisms as a mixed problem of correlation of crank angles and dead center design

Simulation and Experimental Study on Aerospace Push-button Latch of Planar Four-bar Linkage

This paper analyzes the relevant research on push-button quick-release latch, and presents the dynamic model of a typical push-button latch based on a planar four-bar linkage mechanism. ADAMS software was used to simulate the opening and closing performance of the typical push-button latch. The influence of push angle, push position, push speed and push acceleration on the actual opening force measurement of the product was analyzed, as well as the preload test method of the push-button latch, and the sensor method was recommended to measure the preload force, and tested by experiments. Moreover, this paper analyzes the durability test method of push-button latch, uses the sensor to detect the change of opening and closing force in the process of durability test and studies the durability test of typical products.

CAD-Based Design Optimization of Four-Bar Mechanisms: An Emergency Ventilator Case Study

The design optimization of mechanisms is promising as it results in more energy-efficient machines without compromising performance. However, machine builders do not apply state-of-the-art methods, as these algorithms require case-specific theoretical analysis. Moreover, the design synthesis approaches in the literature predominantly utilize heuristic optimizers, leading to suboptimal local minima. This paper introduces a widely applicable workflow, guaranteeing the global optimum. The constraints describing the feasible region of the possible designs are essential to find the global optimum. Therefore, kinematic analysis of the point-to-point planar four-bar mechanism is discussed. Within the feasible design space, objective value samples were generated through the CAD multi-body software. These motion simulations determine the required torque to fulfill the movement for a combination of design parameters. This replaces the cumbersome analytic derivation of the torque. This paper introduces sparse interpolation techniques to avoid brute force sampling of the design space. The advantage of this approach is that it is easily scalable to more design parameters, as the interpolation method minimizes the number of necessary samples. This paper explains the mathematical background of our developed interpolation approach. However, a step-by-step procedure is introduced to allow the employment of the interpolation technique by machine designers without the necessity to understand the underlying mathematics. Finally, the mathematical expression, obtained from the interpolation, enables applying global optimizers. In a case study of an emergency ventilator mechanism with three design parameters, 1870 CAD motion simulations allowed reducing the RMS torque of the mechanism by 67%.

Type synthesis and performance analysis of manipulators with shape adaptability

Manipulators have attracted wide attention in recent years because they are simple and easy to control when grasping objects in space. However, there are not many theoretical researches on manipulator at present. Therefore, based on the principle of simple operation and low cost, a manipulator with high versatility, high flexibility, diverse movement modes, and shape adaptability has laid a solid theoretical foundation and practical significance for the innovative development of robot. In this paper, a 4-RRS& planar four-bar mechanism with bifurcation motion is proposed based on the finite screw theory. The degrees of freedom of the mechanism are analyzed by using the screw theory. Then the closed-loop vector method and instantaneous screw method are used to establish the analytical expression and the velocity Jacobian matrix between the motor actuation angle and the moving platform, respectively. Finally, on the basis of kinematic analysis, the SolidWorks and Matlab software are used to verify the kinematic simulation of the mechanism, so as to ensure the rationality of the mechanism motion and the correctness of the theoretical derivation.

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.

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.

A design approach for gravity compensators using planar four-bar mechanisms and a linear spring

This paper presents a design approach for gravity compensators using planar four-bar mechanisms and a linear spring. This work enables the development of a class of gravity compensators encompassing 42 different types, which are characterized by high performance and kinematic simplicity. The gravity compensators are constructed by combining planar four-bar mechanisms with a rotating mass and attaching a linear spring to each mechanism, then permuting the springs. The parameters of the gravity compensators are derived from an optimization procedure that minimizes the actuator torque within a specified balancing zone. The performances of the gravity compensators were demonstrated via both numerical examples and experiments. The results showed their design feasibilities and high performances in which a torque reduction rate of 87.8% was practically achieved. Lastly, an application of the proposed gravity compensators to serial robots is described. It was found that the actuator torque of a serial robot over a prescribed workspace could theoretically be reduced by 98.2%. A prototype of a serial robot was also built to validate the applicability of the gravity compensators.

Development and experimental evaluation of a walking assist device using a cane movement as input

In today's aging society, a variety of walking aids have been developed for the elderly or those who have difficulty walking due to injury. The main type of walking aids used in daily life are inexpensive simple walking aids such as canes, etc. Simple walking aids are used to reduce the load on the legs by placing a part of the body weight on the cane or walker. If the user relies on these devices, the user's posture when walking may become unsteady, and a load different from the original walking may be applied to the user. For the reason, the development of products with simple structures is desired to reduce the cost of equipment for the widespread use of welfare machines. Therefore, in this research, authors developed an inexpensive and lightweight walking aid using a link mechanism that does not require electronic control. The purpose of this research is to develop a walking aid for dynamic gait that can be used by more people. The device does not require electronic control, and the user drives the device with his/her own arm movements. The device is a planar four-bar mechanism that converts rotational motion into oscillatory motion to improve the transmission of force. An experimental comparison was made between a device with a planar six-bar mechanism, which was the subject of a previous study, and a device with a planar four-bar mechanism, in which the mechanism constants were changed.

Development and mechanical evaluation of walking assist device using a cane movement as input

In today's aging society, a variety of walking aids have been developed for the elderly or those who have difficulty walking due to injury. The main type of walking aids used in daily life are inexpensive simple walking aids such as canes, etc. Simple walking aids are used to reduce the load on the legs by placing a part of the body weight on the cane or walker. If the user relies on these devices, the user's posture when walking may become unsteady, and a load different from the original walking may be applied to the user. For the reason, the development of products with simple structures is desired to reduce the cost of equipment for the widespread use of welfare machines. Therefore, in this research, authors developed an inexpensive and lightweight walking aid using a link mechanism that does not require electronic control. The purpose of this research is to develop a walking aid for dynamic gait that can be used by more people. The device does not require electronic control, and the user drives the device with his/her own arm movements. The device is a planar four-bar mechanism that converts rotational motion into oscillatory motion to improve the transmission of force. The mechanism constants of a device with a planar six-bar mechanism, which was the subject of a previous study, were changed, and the auxiliary effects were compared with those of a planar four-bar mechanism.

Nine-Parameter Path Synthesis of Planar Four-Bar Mechanism with the Aid of the General Equation of Coupler Curve

Nine-Parameter Path Synthesis of Planar Four-Bar Mechanism with the Aid of the General Equation of Coupler Curve

Assessment of computer vision methods for motion tracking of planar mechanisms

One of the main challenges on the use of planar mechanisms is to verify and monitor that the trajectories described by the mechanism correspond to those originally required. However, very few research studies have focused on tracking and monitoring the motion of target points located on the mechanisms during operation conditions. In this paper, a comparative study to evaluate the performance of several computer vision methods (CVMs) when used in motion tracking of planar mechanisms is presented. The aim is to compare and identify the best CVM, in terms of precision, speed, low cost, and computational performance, to track the movement of planar mechanisms. For this purpose, a case study corresponding to a planar four-bar mechanism is selected and analysed. The results show that the vision methods based on the homogeneous and non-homogeneous solution of the camera calibration matrix are a technological alternative for monitoring motion trajectories of planar mechanisms.

Design and analysis of bionic cobweb Umbrella-Type deployable mechanism

Based on the simplified mapping model of the geometric characteristics of a cobweb structure, a new umbrella-type deployable mechanism with a planar four-bar crank slider mechanism as the deployable unit is proposed. First, the model is statically analyzed and optimized using the Ansys Workbench software, and the optimal ratio of the spiral thread spacing in the model is determined. Additionally, the stiffness matrix of the cobweb rigid frame model is established, and the optimal angle between the spiral threads is determined using the matrix displacement method. Then, according to the optimized model angle and ratio, a new umbrella-type deployable mechanism is proposed, and its static performance is simulated and analyzed. The results show that the strength of the umbrella-type developable mechanism is improved, and the movement process is simulated to verify the effectiveness of the model deployment and folding process.

Dynamic investigation of a spatial multi-body mechanism considering joint clearance and friction based on coordinate partitioning method

The dynamic response of the model, which is the series connection of a planar four-bar mechanism and a spatial RSSR mechanism, is analyzed considering revolute joint clearance and friction. A non-holonomic constraint equation is proposed to solve the Euler angles. The dynamic equations are established by combining the Lagrange equation with the modified contact model and the LuGre friction model. A dynamic solution program based on the coordinate partitioning method is designed to solve the dynamic equations. The paper verifies the correctness and applicability of the solution program by comparing the numerical calculation results with Adams simulation. Compared with the results of eccentricity, it is found that the maximum penetration is very sensitive to the change of the slider speed rather than the clearance. The equivalent damping coefficient proposed by authors not only represents whether a collision occurs, but reflects the hysteresis caused by damping. The macroscopic manifestation of the up and down oscillation of eccentricity is the swing of the contact point. Besides, the system quickly changes from the collision into the stable state due to considering friction, and the peak value of each collision reduces greatly. Therefore, when the clearance is unavoidable, the clearance joint should be coated with a material with a large friction coefficient and not easy to wear.

A novel optimization-based method to find multiple solutions for path synthesis of planar four-bar and slider-crank mechanisms

The classical method to find possible solutions for path synthesis problem of planar mechanisms is continuation method. However, this method has some disadvantages such as producing unwanted extraneous and degenerate solutions and also producing mechanisms having defects. Moreover, many of the solutions are cognate of each other which can be obtained geometrically. Thus, finding the most feasible solution among all solutions is a cumbersome and time-consuming task. The main purpose of this paper is to explore applicability of heuristic algorithms to find multiple cognate- and defect-free solutions for path synthesis problems of planar four-bar and slider-crank mechanisms. To this aim, a new modified error function and an optimization-based algorithm is presented. The gravitational search algorithm (GSA) is utilized to minimize the modified error function. Efficiency of the method is proved through five case studies for path synthesis of four-bar and slider-crank mechanisms with and without prescribed timing.

Application of Gauss principle of least constraint in multibody systems with redundant constraints

Redundancy in the constrained mechanical systems often occurs in complex multibody mechanic systems in the existence of excessive constraints and singular positions due to system motion. In this work, Gauss principle of least constraint (GPLC) is applied to solve the dynamic motion of system with redundant constraints without changing the physics of system. Furthermore, the particle swarm optimization method is used to handle the minimization optimization problem. Eventually, the effectiveness of GPLC is validated through the dynamic modelling and simulation of two numerical examples (a planar four-bar mechanism and a spatial parallelogram mechanism). The simulation results are analyzed and compared with those obtained from Udwaia-Phohomsiri formulation and augmented Lagrangian formulation, in terms of constraint violation, computational efficiency and variation of the mechanical energy. From the viewpoint of computational efficiency and accuracy, GPLC can be regarded as a practical real-time simulation method for multibody systems with redundant constraints.

Pareto Optimal Balancing of Four-bar Mechanisms Using Multi-Objective Differential Evolution Algorithm

Four-bar mechanisms are widely used in the industry especially in rotary engines. These mechanisms are usually applied for attaining a special motion duty like path generation; their high speeds in the industry cause an unbalancing problem. Hence, dynamic balancing is essential for their greater efficiency. In this research study, a multi-objective differential evolution algorithm is used for Pareto optimization balancing of a four-bar planar mechanism while considering the shaking moment and horizontal and vertical shaking forces as objective functions. This is necessary since the high magnitude of shaking forces and moment affect the fatigue life of the mechanism. The design variables are both kinematic and dynamic parameters of the moving links. The Pareto charts of five-objective optimization exhibit a large number of non-dominated points, which provide more choices for optimal balancing design of the planar four-bar mechanism. A comparison of the results obtained from this study with those reported in the literature shows a significant decrease in shaking forces and shaking moment.

Principal vectors and equivalent mass descriptions for the equations of motion of planar four-bar mechanisms

The use of principal points and principal vectors in the formulation of the equations of motion of a general 4R planar four-bar linkage is shown with two kinds of methods, one that opens kinematic loops and one that does not. The opened kinematic loop approach analyses the moving links as a system with a tree connectivity, introducing reaction forces for closing the loops. Compared with the conventional Newton–Euler method, this approach results in fewer equations and constraint forces, whereas the mass matrix entries remain meaningful, but there is a stronger coupling between the equations. Two equivalent mass formulations for the closed kinematic loop approach are presented, which need not open the loop and introduce loop constraint forces in the equations of motion. With the method of complex joint masses, the mass of the links closing the loops is represented by real and virtual equivalent masses, defining the principal points. The principle of virtual work with the inclusion of inertia terms is used to derive the equations of motion. As an example the dynamic balance conditions of the four-bar linkage are derived. With the method of the equivalent mass matrix it is shown how a constant mass matrix can be used to describe the dynamics of binary links with an arbitrary mass distribution. A four-bar linkage could be modelled with only three truss elements instead of the conventional result with three or more beam elements, which gives a significant reduction of the computational complexity.

On the Solution of Eight-Precision-Point Path Synthesis of Planar Four-Bar Mechanisms Based on the Solution Region Methodology

AbstractIn this paper, the solution region synthesis methodology (abbreviated as SRSM below) for the eight-precision-point path synthesis of planar four-bar mechanisms is presented. The so-called solution region synthesis methodology represents an infinite number of mechanism solutions in a plane, and the solution region is the area where the mechanism solutions are distributed in the plane. The x-coordinate and the y-coordinate of the plane are both taken as the concerned parameters of mechanisms. Furthermore, characteristic curves of mechanisms can be expressed in the plane. In addition, a defect judgment method is proposed, which can be realized in the computer program. The defective solutions can be eliminated efficiently, and the solutions without defects are obtained using the proposed method. After considering and imposing additional design requirements, the linkages of different types and different curve shapes are classified in the solution region. Finally, taking the path generation for eight points as the example, the methodology of establishing the solution region and the feasible solution region are presented, and the synthesis results are illustrated.