Parallelogram Mechanism Research Articles

A modified pseudo-rigid-body modeling approach for compliant mechanisms with fixed-guided beam flexures

Abstract. In the present paper, we investigate a modified pseudo-rigid-body (MPRB) modeling approach for compliant mechanisms with fixed-guided beam flexures by considering the nonlinear effects of center-shifting and load-stiffening. In particular, a fixed-guided compliant beam is modeled as a pair of fixed-free compliant beams jointed at the inflection point, where each fixed-free beam flexure is further modeled by a rigid link connected with an extension spring by a torsion spring, based on the beam constraint model (BCM). Meanwhile, the characteristic parameters of the proposed MPRB model are no longer constant values, but affected by the applied general tip load, especially the axial force. The developed MPRB modeling method is then applied to the analysis of three common compliant mechanisms (i.e. compound parallelogram mechanisms, bistable mechanisms and 1-DOF translational mechanisms), which is further verified by the finite element analysis (FEA) results. The proposed MPRB model provides a more accurate method to predict the performance characteristics such as deformation capability, stiffness variation, as well as error motions of complaint mechanisms with fixed-guided beam flexures, and offers a new look into the design and optimization of beam-based compliant mechanisms.

Dynamic performance of over-constrained planar mechanisms with multiple revolute clearance joints

The clearances of joints in a rigid multibody system may deteriorate the motion accuracy and even cause vibrations, noise and fatigue failure of structures. In over-constrained mechanisms, the number of degree-of-freedoms is more than that of independent coordinates which leads to numerical challenges in solving the underdetermined force equilibrium equations. A comprehensive study on the dynamic model and the performance of an over-constrained planar parallelogram mechanism with multiple clearance joints is presented in this paper. Since a common angular coordinate exists in the clearance joint associated with the redundant constraint, the degree-of-freedoms are revised by eliminating the number of redundant constraints. In planar analysis, the location of mass center and the orientation of the body reference with respect to the inertial frame are selected as the generalized coordinates of the components. Clearance joints are equivalent as the spring-damper elements and the contact forces are introduced into the dynamic equations by force constraints. The developed computational algorithm is implemented by MATLAB and may analyze the dynamic performance of this mechanism due to the elimination of kinematic constraints and the nonlinear contact-impact behavior in the clearance joints. Meanwhile, an orthogonal experimental design based on a quantitative analysis method demonstrates that the clearance size and the location of clearance joints affect the kinematic accuracy and counterbalance moment of the mechanism.

Design and control of a multi-DOF micromanipulator dedicated to multiscale micromanipulation

This paper presents the design, implementation and control of a new piezoelectrically actuated compliant micromanipulator dedicated to multiscale, precision and reliable operations. To begin with, the manipulator is devised to obtain multi degrees of freedom and large workspace ranges. Two-stage amplification mechanisms (consists of the leverage and the rocker mechanisms) and composite parallelogram mechanisms are combined to construct the lower microstage. Meanwhile, the structure design of the upper dual-driven microgripper is based on the bridge-type mechanism and the unilateral parallelogram mechanism. Through finite-element analysis, the structural parameters of the micromanipulator are optimized and the structural interaction performances are examined. Moreover, a cooperative control strategy is proposed to achieve the synchronous control of the motion trajectory, the gripper position and the contact force. Precision motion control in terms of the hysteresis phenomenon and system disturbances is ensured by using an adaptive sliding mode control (SMC). In particular, an improved nonsymmetrical Bouc–Wen model and a fuzzy regulator are proposed in the SMC. Several experimental investigations are conducted to validate the effectiveness of the developed micromanipulator by performing transferring operations of a micro-object. Experimental results demonstrate that the micromanipulator presents good characteristics, and precision and robust operation can be acquired using the cooperative controller.

A Highly-Maneuverable Demining Autonomous Robot: an Over-Actuated Design

Based on the well-known advantages of using an over-actuated mechanism for robots, this research proposes a holonomic highly-maneuverable autonomous robot design for demining service applications. The proposed approach provides an interesting compromise between the design requirements of the demining robot applications and the over-actuated autonomous robots. The robot body is mainly divided into two parts: the first part provides the robot with its required locomotion and it consists of a driving/steering subsystem with four driving wheels (4WD), four steering mechanisms (4SW), and a passive suspension subsystem. The second part is a manipulator with three degrees of freedom that is designed based on two parallelogram mechanisms. The proposed design insures many advantages over existing designs, including stability, maneuverability, autonomous navigation, and simplicity of the control effort constraints. The robot model and its corresponding stability analysis were conducted and simulated in order to evaluate the motion of the robot over different environments rough terrains and slanted surfaces. Moreover, a prototype of the proposed robot was developed and built and different types of sensors were used in order to help it take precise actuation decisions for navigation and control. The prototype was experimentally tested for different scenarios and environments in order to validate the proposed design. The testing results demonstrated decent performance of the robot in autonomous navigation and in localizing the detected objects.

Reconfigurable deployable polyhedral mechanism based on extended parallelogram mechanism

This paper dealt with the construction of a novel class of reconfigurable deployable polyhedral mechanisms (RDPMs). A parallelograms mechanism was designed by considering layers of links and size of revolute joints, and extended parallelogram mechanisms (EPaM) were constructed for the first time by inserting angulated elements and scissor-like elements into the parallelogram mechanism. The detailed parameters and magnification ratios of two kinds of EPaMs were calculated. A method was then proposed for constructing RDPMs based on EPaMs. The proposed method can provide more modular linkages for RDPMs, and all polyhedra constituted by regular polygons can be used to construct RDPMs. The obtained RDPMs can be reassembled by increasing or decreasing the number of basic elements to change the sizes beyond their deployment capacity. A prototype of reconfigurable deployable hexahedral mechanism based on EPaMs was fabricated to verify the feasibility of this class of RDPMs, and three reconfigurable deployable hexahedral mechanisms in three sizes based on the prototype were reassembled and tested.

Static stiffness modelling of EAST articulated maintenance arm using matrix structural analysis method

The remote inspection and maintenance of the small pieces in vacuum vessel requires certain accuracy to the serial long-reach robot applied in EAST tokamak. The elastic deformations due to gravity and dynamical forces, however, will cause a big trajectory tracking error to the robot end. Therefore, the error prediction and compensation strategy should always be studied in advance to achieve a high required accuracy. This paper presents a mathematical method to estimate the static stiffness of EAST articulated maintenance arm (EAMA) robot. Firstly, the stiffness matrix of the modular parallelogram mechanism of robot is obtained based on the Matrix Structural Analysis (MSA) method. Considering the real constraint conditions of robot arms, the matrix is further simplified to a final version with minimum dimension to improve the computational efficiency. Secondly, the simulation examples have been given to evaluate the accuracy and reliability of the stiffness equations. And finally, the results show that the presented approach has an acceptable prediction error (less than 5%), which can be applied to other similar robotic systems with long-reach complex links.

Design and analysis of a new flexure-based XY stage

This article presents the design, modeling, and experimental testing of a novel piezo-driven XY stage with parallel, decoupled, and compact kinematic structure. The structural design of the stage is based on a hybrid compliant mechanism employing the right-circular double-rocker mechanism and the leaf-type parallelogram mechanism. The proposed XY stage is capable of producing a large workspace range, an excellent decoupled motion, and a suitable resonant frequency. By means of the pseudorigid-body-model method, the theoretical models of the XY stage are derived. Using the finite element analysis simulations, the optimal structural parameters are acquired, and the theoretical models are analyzed and validated. A prototype of the proposed stage was finally manufactured, and several experimental investigations were performed to validate its performances. The experimental results show that the XY stage has a large amplification ratio of 7.48 and a large workspace range of 150.3 µm × 147.9 µm. In addition, the parasitic motion along the y-axis ( x-axis) accounts for 0.94% (0.74%) of the x-axis ( y-axis) motion, which indicates that the stage possesses excellent decoupling characteristics.

Analysis of Parallelogram Mechanism used to Preserve Remote Center of Motion for Surgical Telemanipulator

This paper presents an analysis of a parallelogram mechanism commonly used to provide a kinematic remote center of motion in surgical telemanipulators. Selected types of parallel manipulator designs, encountered in commercial and laboratory-made designs described in the medical robotics literature, will serve as the research material. Among other things, computer simulations in the ANSYS 13.0 CAD/CAE software environment, employing the finite element method, will be used. The kinematics of the solution of manipulator with the parallelogram mechanism will be determined in order to provide a more complete description. These results will form the basis for the decision regarding the possibility of applying a parallelogram mechanism in an original prototype of a telemanipulator arm.

The Differential Method for Force Measurement Based on Electrostatic Force

The small force measurement is very important with development of the technology. The electrostatic force is adopted, in which a pair of coaxial cylindrical capacitors generate the electrostatic force when a voltage is applied across the inner and outer electrodes. However, the measured force will be covered by noise (creep, ground vibration, and air flow) and could not be measured accurately. In this paper, we introduce the differential method to reduce the effect of noise. Two identical parallelogram mechanisms (PM) serve as the mechanical spring. One of the PM serves as the reference and another serves as the force sensor. The common signal will be offset, and the difference signal will serve as output. In this way, the effect of the creep will be reduced. The measurement system of the electrostatic force was characterized by applying mechanical forces of known magnitude via loading weights of calibrated masses. The uncertainty from voltage, laser interferometer, and capacitance gradient was estimated. For the measured force, the relative uncertainty is less than 4% (kp=2).

A novel flexure beam module with low stiffness loss in compliant mechanisms

Flexure mechanisms provide guided motion via elastic deformation of thin beams. Due to the employment of compliant elements, these mechanisms cannot sufficiently maintain acceptable constraint stiffness level in the entire range of motion. The stiffness deterioration afflicts the performance of flexure mechanisms in terms of motion range, accuracy and constraint characteristics. This paper presents a novel flexure beam module with improved constraint behavior in beam-based flexure mechanisms. The proposed module alleviates the problem of stiffness loss in large displacements and provides a better motion performance. The mathematical model governing the static behavior of the module is developed using the principle of virtual work. The geometric nonlinearity associated with large midplane stretching is taken into account. Closed-form solutions are derived for load-displacement relationships, providing a powerful design tool for the novel flexure. Also a nonlinear expression is obtained for the strain energy of the flexure in terms of end displacements. The functionality of the presented module is exploited in a multi-beam parallelogram mechanism. The constraint behavior of the parallelogram is analytically quantified and considerable improvements in stiffnesses and error motions are observed. The analytical results provided in this paper are verified via finite element simulations. The proposed novel module can be used as the building block of more complex flexures to improve their stiffness characteristics, diminish their error motions and widen their stability region.

Bi-BCM: A Closed-Form Solution for Fixed-Guided Beams in Compliant Mechanisms

A fixed-guided beam, with one end is fixed while the other is guided in that the angle of that end does not change, is one of the most commonly used flexible segments in compliant mechanisms such as bistable mechanisms, compliant parallelogram mechanisms, compound compliant parallelogram mechanisms, and thermomechanical in-plane microactuators. In this paper, we split a fixed-guided beam into two elements, formulate each element using the beam constraint model (BCM) equations, and then assemble the two elements' equations to obtain the final solution for the load–deflection relations. Interestingly, the resulting load–deflection solution (referred to as Bi-BCM) is closed-form, in which the tip loads are expressed as functions of the tip deflections. The maximum allowable axial force of Bi-BCM is the quadruple of that of BCM. Bi-BCM also extends the capability of BCM for predicting the second mode bending of fixed-guided beams. Besides, the boundary line between the first and the second modes bending of fixed-guided beams can be easily obtained using a closed-form equation. Bi-BCM can be immediately used for quick design calculations of compliant mechanisms utilizing fixed-guided beams as their flexible segments (generally no iteration is required). Different examples are analyzed to illustrate the usage of Bi-BCM, and the results show the effectiveness of the closed-form solution.

Al-Zahrawi: A Telesurgical Robotic System for Minimal Invasive Surgery

Surgical robots provide various advantages, such as improved precision and dexterity, over conventional surgical procedures and have been extensively studied in the last decade. Many surgical robots have been recently developed and described in the literature. However, given their multidisciplinary nature, due to the involvement of medical surgery, electrical engineering, mechanical engineering, and computer science, very few existing documents provide a system design perspective of a complete surgical robot. We tend to fill this gap by presenting the complete system-level design of Al-Zahrawi, which is a new telesurgical robotic system. The Al-Zahrawi system is mainly composed of two parts, i.e., a master console and a slave console, which are connected through a communication link. The master console consists of master manipulators (MMs), visual information presentation apparatus, and foot pedals. The slave console is primarily composed of three slave manipulators (SMs): The left and right manipulators are equipped with surgical instruments, whereas the middle one holds the endoscope. All the manipulators utilize the modified double parallelogram mechanism to achieve the remote center of motion. The distinguishing features of this system include: 1) a custom-made simple-in-construction user-friendly MMs; 2) a modular SM, with an interchangeable instrument module that does not contain any electronic circuitry and thus can be completely sterilized with ease; and 3) the availability of an independent forceps jaw movement, which increases the dexterity of the surgical tool tip without using the wrist mechanism.

DESIGN, FABRICATION, AND TEST OF A NOVEL CLAMPER FOR AORTIC CROSS-CLAMPING IN MINIMALLY INVASIVE CARDIAC SURGERY

One of the main procedures in the most minimally invasive cardiothoracic surgery is clamping the ascending aorta to disconnect the heart from circulation. In this paper, a new aortic clamping instrument which is applicable in minimally invasive cardiac surgery has been presented. The instrument consists of a parallelogram mechanism for opening and closing the jaws, a detachable holder with a two degree of freedom joint that makes the precise position and orientation of the jaws and leaves the clamping component in the patient’s body to make the inserting port free, and a handle for easy manipulation. In vitro test has been performed to evaluate the performance of the clamper compared to the conventional clampers. For this purpose, the force required for aortic cross-clamping and the maximum aortic displacement have been studied in four groups including parallel clamper and conventional clamper with angles of 1[Formula: see text], 2[Formula: see text], and 3[Formula: see text] between jaws, with 10 bovine aorta specimens in each group. These experiments show that the amount of required force for cross-clamping by using the parallel clamper, is statistically significant ([Formula: see text]) compared with the conventional clampers. Also, the increase of angle between jaws makes a significant increase in the percentage of aortic displacement.

Development of an Electromagnetic Actuated Microdisplacement Module

This paper presents the mechanical design and control system design of an electromagnetic actuator-based microdisplacement module. The microdisplacement module composed of a symmetrical leaf-spring parallelogram mechanism and an electromagnetic actuator. The characteristics of the mechanism in terms of stiffness and natural frequencies are derived and verified. Both leakage flux and core inductance are taken into consideration during modeling the mathematic model of the electromagnetic actuator, and based on which, the system dynamic model is established. Due to the nonlinearity characteristics of the system, a dynamic sliding-mode controller is designed without linearizing the system dynamics. A prototype of the microdisplacement module is fabricated, and the parameters of the system are identified and calibrated. Finally, the designed dynamic sliding-mode controller is applied; step response and tracking performance are studied. Experimental results demonstrate that a submicrometer accuracy can be achieved by the module, which validate the effectiveness of the proposed mechanism and controller design as well. The research results show that the electromagnetic actuator-based module can be extended to wide applications in the field of micro/nanopositioning and manipulation.

Structure-control design of a mechatronic system with parallelogram mechanism using an estimation of distribution algorithm

ABSTRACTIn this paper, a structure-control design methodology for simultaneously optimizing both mechanical structure and control of a parallelogram linkage robot is proposed. It takes into count the dynamical model and the mechanical parameters for the optimization process along with the controller. Thus, proportional-integral-derivative (PID) control and geometric variables are optimized in a simultaneously way. Through the concurrent procedure an optimal combination of the robot structure and controller gains is obtained. The global optimization problem is tackled by using an estimation of distribution algorithm (EDA) based on the Boltzmann distribution. The EDA seeks for the global optimum by estimating and sampling a probability distribution. The proposed methodology is verified through simulation experiments and applied to the design process of a parallelogram linkage system. The results obtained in experiments show the effectiveness of the proposal. This approach is generic and could be applied to other mechanisms in similar way when for concurrent process both kinematic and dynamic models are available along with the controller. In particular, the results are promising when the optimization parameters are uncorrelated, namely control and mechanical parameters.

Extended Static Modeling and Analysis of Compliant Compound Parallelogram Mechanisms Considering the Initial Internal Axial Force*

Extended nonlinear analytical modeling and analysis of compound parallelogram mechanisms are conducted in this paper to consider the effect of the initial internal axial force. The nonlinear analytical model of a compound basic parallelogram mechanism (CBPM) is first derived incorporating the initial internal axial force. The stiffness equations of compound multibeam parallelogram mechanisms (CMPMs) are then followed. The analytical maximal stress under the primary actuation force only is also derived to determine the maximal primary motion (motion range). The influence of initial internal axial forces on the primary motion/stiffness is further quantitatively analyzed by considering different slenderness ratios, which can be employed to consider active displacement preloading control and/or thermal effects. The criterion that the primary stiffness may be considered “constant” is defined and the initial internal axial force driven by a temperature change is also formulated. A physical preloading system to control the initial internal axial force is presented and testing results of the object CBPM are compared with theoretical ones.

Simplified modelling and development of a bi-directionally adjustable constant-force compliant gripper

This paper proposes the design of a wholly mechanical constant-force gripper that can accommodate the imprecise manipulation of brittle/delicate objects by the actuation. This was achieved by designing a constant-force mechanism as the jaw that allowed a constant force to be applied to the grasping objects regardless of the displacement of the mechanism. The constant-force mechanism is attached to the end effector of the gripper via a parallelogram mechanism which ensures that the jaws remain in parallel. The constant-force mechanism combines the negative stiffness of a bistable mechanism and the positive stiffness of a linear spring to generate a constant force output. By preloading the positive stiffness mechanism, the magnitude of the constant force can be adjusted to be as low as zero. The constant-force mechanism has been fully modelled and simulated using finite element analysis. A normalised force-displacement curve has been developed that allows to obtain the simplified analytical negative stiffness of the bistable mechanism. The design formulation to find the optimal configuration that produces the most constant force has been developed. Illustrated experiments prove the concept of the design although the discrepancies between finite element analysis results and testing results exist due to bistable beam manufacturing error.

An Approach Regarding Windshield Wiper Mechanism Design

This research presents the use of a computer oriented numerical approach in the characterization of a parallelogram mechanism used on automobile windscreen wipers. The aim is to perform a kinetostatic analysis for obtaining through numerical simulations the joint reaction forces for a parameterized mechanism. Based on a combination between classical methods and computer simulations using Multi-body System method, the friction forces between wipers blades and windshield will be evaluated. The obtained results add new contributions on automobile windshield wiper mechanism design and analysis.

Development and precision position/force control of a new flexure-based microgripper

This paper presents the design, modeling and position/force control of a new piezo-driven microgripper with integrated position and force sensors. The structural design of the microgripper is based on double amplification mechanisms employing the bridge-type mechanism and the parallelogram mechanism. The microgripper can generate a large gripping range and pure translation of the gripping arm. Through the pseudorigid-body-model method, theoretical models are derived. By means of several finite-element analysis simulations, the optimal structural parameters for the microgripper are acquired and the theoretical models are analyzed and validated. Furthermore, to improve the performance of the microgripper, a new hybrid position/force control scheme employing a nonlinear fuzzy logic controller combined with an incremental proportional-integral controller is presented. The control scheme is capable of regulating the position and the gripping force of the microgripper simultaneously. Experimental investigation and validation were performed and the experimental results verify the effectiveness of the developed structural design and the proposed hybrid control scheme.

Nonlinear Analytical Modeling and Characteristic Analysis of a Class of Compound Multibeam Parallelogram Mechanisms

This paper deals with nonlinear analytical models of a class of compound multibeam parallelogram mechanisms (CMPMs) along with the static characteristic analysis. The CMPM is composed of multiple compound basic parallelogram mechanisms (CBPMs) in an embedded parallel arrangement. First, nonlinear analytical models for the CBPM are derived using the free-body diagram method through appropriate approximation strategies. The nonlinear analytical models of the CMPM are then derived based on the modeling results of the CBPM. Nonlinear finite element analysis (FEA) comparisons, experimental testing, and detailed stiffness analysis for the CBPM are finally carried out. It is shown that the analytical primary motion model agrees with both the FEA model and the testing result very well but the analytical parasitic motion model deviates from the FEA model over the large primary motion/force. It is also shown from the analytical characteristic analysis that the primary translational stiffness increases with the primary motion but the parasitic motion stiffness decreases with the primary motion, and the stiffness ratio of the parasitic motion stiffness to the primary translation stiffness also decreases with the primary motion. It is found that the larger the beam slenderness ratio is, the larger the stiffness or stiffness ratio is, and the more apparent the change of the stiffness or stiffness ratio is. The varied stiffness ratio indicates the mobility change of the CBPM.