Pseudo-rigid-body Model Research Articles

Design of a Novel Dual-Axis Micromanipulator With an Asymmetric Compliant Structure

This paper presents a novel piezoelectrically actuated dual-axis micromanipulator with an asymmetric compliant structure. The mechanical design of the micromanipulator is first presented. A novel guiding bridge-type mechanism was proposed and utilized in the left part of the micromanipulator to improve the dynamic performance of the micromanipulator. The analytical model has been established based on the pseudorigid-body model and matrix-based compliance modeling method. The kinematic and the precision of the micromanipulator have been analyzed, and the input and output couplings have been investigated. The prototype of the micromanipulator has been fabricated by wire electrodischarge machining. Then, open-loop experimental tests have been performed. The experimental results match well with the analytical calculation, and the amplification ratios are 11.12 and 4.64 for the left part and right part, respectively. Proportional-integral controller has been used to regulate the output displacement and grasping force, and a series of closed-loop experiments have been conducted to investigate the performance of the micromanipulator. The results show that the position resolution for both the right and left parts is 0.15 μm, and the force resolution is 4 mN.

Vision-Based 3-D Control of Magnetically Actuated Catheter Using BigMag—An Array of Mobile Electromagnetic Coils

Automated steering of endovascular catheters has a potential of improving the outcome of minimally invasive surgical procedures. Nevertheless, actuation, tracking, and closed-loop position control of catheters remain a challenge. In this study, we present a modular framework for a three-dimensional (3-D) position control of magnetically actuated endovascular catheter. The catheter is fitted with a permanent magnet and deflected using externally generated magnetic field provided by BigMag—An array of mobile electromagnets. Pseudorigid-body modeling is used to formulate an inverse-model closed-loop position controller of the catheter. The shape feedback is reconstructed from a 3-D point cloud of catheter silhouette, obtained using stereo vision. Magnetic actuation is enabled using an inverse field map technique, mapping the reference magnetic field to BigMag configuration variables. The framework is tested in a series of experiments. The inverse map is validated, showing a mean magnetic field error of 2.20%. The accuracy of the shape reconstruction algorithm is 0.59 mm. Finally, the magnetically actuated catheter is steered across a series of trajectories with maximum reported catheter deflection of 68.43 $^\circ$ and maximum tip speed of 5 mm/s. Across all trajectories, the best control performance metrics are the mean error of 0.57 mm and the RMS error of 0.77 mm.

Dynamic modeling and performance of compliant mechanisms with inflection beams

A study on the dynamic modeling and performance for compliant mechanisms with inflection beams is presented. Based on the pseudo-rigid-body model (PRBM), a 5R Dynamic PRBM (5R D-PRBM) is proposed for the flexural beams with inflection points. The dynamic equation of the 5R D-PRBM is derived using Lagrangian equation. Numerical investigations on the dynamic responses of the flexural beam with an inflection point are presented by the 5R D-PRBM. The advantage of the new model is illustrated comparing with ADAMS simulation. An example of compliant parallel-guiding mechanism is presented using the 5R D-PRBM.

A roller posture adjustment device with remote-center-of-motion for roll-to-roll printed electronics

Nonuniform web tension has a great negative effect on product quality of roll-to-roll printed electronics. In this paper, a roller posture adjustment device with remote-center-of-motion (RCM) characteristic is proposed to guarantee web tension uniformity. The device combines a high-stiffness spherical air bearing (SAB) and a multi-degree-of-freedom flexure-based mechanism. The nonuniform web tension in lateral direction can be divided into an equivalent force and two equivalent moments. The equivalent moments are caused by the nonuniformity of the web tension. By adjusting the roller angle around y and z-axes, the equivalent moments can be eliminated to guarantee the web tension uniformity. The multi-DOF flexure-based mechanism is composed of a linear mechanism, a rotary mechanism and a 3-DOF off-plane mechanism. Besides, the RCM characteristic of the proposed device is realized to eliminate extra parasitic movement when the roller posture is changed. Based on pseudo-rigid-body model (PRBM) method, the theoretical analysis is conducted to evaluate the kinematics, stiffness and dynamics of the device. Moreover, the parameter optimization is conducted to maximize the first two resonance frequencies of the system. After that, finite element analysis is conducted to validate the established models. Finally, a prototype of the proposed device is fabricated performance verification. The experimental results show that the proposed device has a workspace of 10.22 mrad and 8.16 mrad about two working axes with center shifts of the RCM point less than 0.75%, which demonstrate the superior property of the proposed device.

Recursive Least Squares Filtering Algorithms for On-Line Viscoelastic Characterization of Biosamples

The mechanical characterization of biological samples is a fundamental issue in biology and related fields, such as tissue and cell mechanics, regenerative medicine and diagnosis of diseases. In this paper, a novel approach for the identification of the stiffness and damping coefficients of biosamples is introduced. According to the proposed method, a MEMS-based microgripper in operational condition is used as a measurement tool. The mechanical model describing the dynamics of the gripper-sample system considers the pseudo-rigid body model for the microgripper, and the Kelvin–Voigt constitutive law of viscoelasticity for the sample. Then, two algorithms based on recursive least square (RLS) methods are implemented for the estimation of the mechanical coefficients, that are the forgetting factor based RLS and the normalised gradient based RLS algorithms. Numerical simulations are performed to verify the effectiveness of the proposed approach. Results confirm the feasibility of the method that enables the ability to perform simultaneously two tasks: sample manipulation and parameters identification.

A CAD/CAE integration framework for analyzing and designing spatial compliant mechanisms via pseudo-rigid-body methods

Abstract Compliant Mechanisms (CMs) are currently employed in several engineering applications requiring high precision and reduced number of parts. For a given mechanism topology, CM analysis and synthesis may be developed resorting to the Pseudo–Rigid Body (PRB) method, in which the behavior of flexible members is approximated via a series of rigid links connected by spring-loaded kinematic pairs. From a CM analysis standpoint, the applicability of a generic PRB model requires the determination of the kinematic pairs’ location and the stiffness of a set of generalized springs. In parallel, from a design standpoint, a PRB model representing the kinetostatic behavior of a flexible system should allow to compute the flexures’ characteristics providing the desired compliance. In light of these considerations, this paper describes a Computer-Aided Design/Engineering (CAD/CAE) framework for the automatic derivation of accurate PRB model parameters, on one hand, and for the shape optimization of complex-shape flexures comprising out-of-plane displacements and distributed compliance. The method leverages on the modelling and simulation capabilities of a parametric CAD (i.e. PTC Creo) seamlessly connected to a CAE tool (i.e. RecurDyn), which provides built-in functions for modelling the motion of flexible members. The method is initially validated on an elementary case study taken from the literature. Then, an industrial case study, which consists of a spatial crank mechanism connected to a fully-compliant four-bar linkage is discussed. At first, an initial sub-optimal design is considered and its PRB representation is automatically determined. Secondly, on the basis of the PRB model, several improved design alternatives are simulated. Finally, the most promising design solution is selected and the dimensions of a flexure with non-trivial shape (i.e. hybrid flexure) is computed. This technique, which combines reliable numerical results to the visual insight of CAD/CAE tools, may be particularly useful for analyzing/designing spatial CMs composed of complex flexure topologies.

A Versatile 3R Pseudo-Rigid-Body Model for Initially Curved and Straight Compliant Beams of Uniform Cross Section

Rigid-body discretization of continuum elements was developed as a method for simplifying the kinematics of otherwise complex systems. Recent work on pseudo-rigid-body (PRB) models for compliant mechanisms has opened up the possibility of using similar concepts for synthesis and design, while incorporating various types of flexible elements within the same framework. In this paper, an idea for combining initially curved and straight beams within planar compliant mechanisms is developed to create a set of equations that can be used to analyze various designs and topologies. A PRB model with three revolute joints is derived to approximate the behavior of initially curved compliant beams, while treating straight beams as a special case (zero curvature). The optimized model parameter values are tabled for a range of arc angles. The general kinematic and static equations for a single-loop mechanism are shown, with an example to illustrate accuracy for shape and displacement . Finally, this framework is used for the design of a compliant constant force mechanism to illustrate its application, and comparisons with finite element analysis (FEA) are provided for validation.

A Compliant Micro Frequency Quadrupler Transmission Utilizing Singularity

This paper presents a method for the design of compliant micro transmission mechanisms which multiply the motion frequency of a cyclic input motion. Compliant embodiments are generated based on exploiting the singularity in a double-slider mechanism, which provides building blocks with a frequency multiplication factor of two. It is shown that the proposed building blocks can be concatenated for higher frequency multiplication ratios, and that the maximum number of blocks is limited by the desired travel range of the output. The input-output kinematics and the different stiffness characteristics of the building blocks are discussed based on pseudo-rigid-body model (PRBM). To validate the building block approach, a compliant micro transmission mechanism is presented which quadruples the frequency of a cyclic rectilinear input motion. Furthermore, a micro scale prototype was dimensioned and fabricated out of silicon using deep reactive ion etching to evaluate the design experimentally and validate the PRBM and finite element models. [2017–0318]

A new bi-directional giant magnetostrictive-driven compliant tensioning stage oriented for maintenance of the surface shape precision

Membrane mirror, known for its perspicuous feature of light weight, high packaging efficiency, low manufacturing cost and etc., has been widely used in the precision optical instruments, such as the primary mirror applied on a space telescope. However, how to maintain the membrane mirror's surface shape precision at a high level is still a challenging problem. Therefore, a bi-directional giant magnetostrictive-driven compliant tensioning stage is proposed in this research, and the basic performance of the stage is studied through theoretical analysis, numerical simulation and experimental investigations. First, the performance requirements and conceptual design are presented and illustrated in detail. Second, the Pseudo Rigid Body Model method is selected as the basis of further investigating the stage and the dynamic model is established through Lagrange's equation. Meanwhile, numerical simulations are performed to analyze the basic performances. Finally, a prototype is manufactured and based on this device, some experiments are conducted. The results indicate that the developed tensioning stage is able to achieve the desired capability and could effectively maintain the surface shape precision.

Damped circular hinge with integrated comb-like substructures

Damping plays an important role in suppressing modal vibration in a flexure-based mechanism due to its lightly damping characteristics. This paper develops a novel damped circular hinge with integrated comb-like substructures, and derives a mathematical model of loss factor of the flexure hinge and builds its pseudo-rigid body model with damping. The damped flexure hinges can be fabricated in a hybrid process with additive material manufacturing or mounting, and damping-material filling by means of some designed aided tools. For the actual fabricated damped circular hinges, their modal loss factors in a specified sandwiched-damping-layer configuration are obtained based on experimental modal analysis, as indicate that sandwiched damping can effectively suppress the bending modal vibration and the damping can be reinforced progressively with a damping-layer number. Meanwhile, based on finite element analysis, loss factor of the damped flexure hinge and its mathematical model are verified. The actual and simulation experimental results indicate that the presented comb-like damped substructures can be effectively functioned as a modular damper for a circular hinge and the damped flexure hinge can be designed independently of its damping and stiffness when low elastic viscoelastic material adopted.

Soft Gripper using Variable Stiffness Mechanism and Its Application

Soft robots have advantages such as low weight and compact size compared to rigid robots. Variable stiffness is one of the key methods of improving the performance of a soft robot. The soft gripper grasps objects of various shapes or sizes based on the variable stiffness. In a previous study, we validated the variable stiffness mechanism where flexible and rigid segments were connected alternately in series. This paper presents a soft variable stiffness gripper that can be used to control the stiffness by pulling tendons. The soft gripper has three variable stiffness structures acting as fingers and the stiffness can be controlled using two motors by winding tendons. To understand the tendency of the stiffness variation and determine the design parameters, a compliant mechanism was developed using a pseudo-rigid-body model (PRBM). The experimental results show that the difference between the lowest and highest stiffness values of the fabricated variable stiffness gripper was 5.6 times the original. Similarly, the difference in the gripping weight was 19 times. Using the experimental results, the variable stiffness gripper can be designed and manufactured based on the required stiffness and used to grip various types of objects.

A Novel Model to Simulate Flexural Complements in Compliant Sensor Systems.

The main challenge in analyzing compliant sensor systems is how to calculate the large deformation of flexural complements. Our study proposes a new model that is called the spline pseudo-rigid-body model (spline PRBM). It combines dynamic spline and the pseudo-rigid-body model (PRBM) to simulate the flexural complements. The axial deformations of flexural complements are modeled by using dynamic spline. This makes it possible to consider the nonlinear compliance of the system using four control points. Three rigid rods connected by two revolute (R) pins with two torsion springs replace the three lines connecting the four control points. The kinematic behavior of the system is described using Lagrange equations. Both the optimization and the numerical fitting methods are used for resolving the characteristic parameters of the new model. An example is given of a compliant mechanism to modify the accuracy of the model. The spline PRBM is important in expanding the applications of the PRBM to the design and simulation of flexural force sensors.

Design and analysis of a compliant variable-diameter mechanism used in variable-diameter wheels for lunar rover

Variable-diameter wheels have two limited working statuses: the unfolded limit rimless wheel and the folded rigid circular wheel. These can solve the contradiction between tractive performance and the limited spacecraft volume of the lunar rover. The variable-diameter mechanism proposed here is the most critical part. It allows the wheel to transform its structure using expansion-retraction motion and to possess excellent running performance. A novel compliant mechanism configuration with helical torsion springs is introduced, along with its mechanism principles. Based on two extreme wheel statuses, a two-position motion generation using nonlinear optimization synthesis is used to determine the dimensional parameters of the mechanism. The load-deflection behavior is derived by developing a pseudo-rigid-body model for the mechanism. Load-deflection relationships obtained from the pseudo-rigid-body model are compared with the results of finite element analysis (FEA) simulations. The results show that the predictions made by the pseudo-rigid-body model (PRBM) are in good agreement. Overall, the design and analysis approaches proposed here are applicable for variable-diameter mechanisms. In addition, the load-deflection relationships presented can provide theoretical references for the variable control of the wheel diameter.

Innovative Silicon Microgrippers for Biomedical Applications: Design, Mechanical Simulation and Evaluation of Protein Fouling

The demand of miniaturized, accurate and robust micro-tools for minimally invasive surgery or in general for micro-manipulation, has grown tremendously in recent years. To meet this need, a new-concept comb-driven microgripper was designed and fabricated. Two microgripper prototypes differing for both the number of links and the number of conjugate surface flexure hinges are presented. Their design takes advantage of an innovative concept based on the pseudo-rigid body model, while the study of microgripper mechanical potentialities in different configurations is supported by finite elements’ simulations. These microgrippers, realized by the deep reactive-ion etching technology, are intended as micro-tools for tissue or cell manipulation and for minimally invasive surgery; therefore, their biocompatibility in terms of protein fouling was assessed. Serum albumin dissolved in phosphate buffer was selected to mimic the physiological environment and its adsorption on microgrippers was measured. The presented microgrippers demonstrated having great potential as biomedical tools, showing a modest propensity to adsorb proteins, independently from the protein concentration and time of incubation.

A new pseudo-rigid-body model approach for modeling the quasi-static response of planar flexure-hinge mechanisms

In this paper a new pseudo-rigid-body model (PRBM) of flexure hinges used in planar flexure-hinge mechanisms with small deformations is presented. Unlike the 1-DOF freedom PRBM used in the existing literature, the PRBM proposed has 3-DOF (degrees of freedom). Using the 3-DOF PRBM of flexure hinges, planar flexure-hinge mechanisms can be represented as rigid multibody systems whose adjacent rigid bodies are connected by 3-DOF joints. After applying this modeling procedure, the principle of virtual work yields a matrix relation for the determination of the quasi-static responses of a flexure mechanism due to external loads. The validity and accuracy of the approach for quasi-static analysis of planar flexure-hinge mechanisms based on the 3-DOF PRBM are examined using the examples of two types of compliant mechanisms: RRR and 3-RRR compliant micro-motion stages.

A Fully Compliant Homokinetic Coupling

This paper introduces a homokinetic coupling, a constant velocity universal joint (CV joint), which is fully compliant and potentially monolithic. The proposed compliant design can accommodate high misalignment angles between the input and the output rotational axes. Additional kinematic constraints are applied to well-known Double Hooke's universal joint, to guarantee a one-to-one constant velocity rotation transmission for all different misalignment angles. The influence of the extra constraints on degrees-of-freedom (DOF) of the mechanism is studied using screw theory. Furthermore, it was shown that the mechanism is yet a 1DOF linkage for rotation transmission and a 2DOF rotational joint as all universal joints. The kinematics of the mechanism is studied, and constant velocity conditions are identified. The pseudo-rigid-body model (PRBM) of the new angled arrangement of the Double Hooke's universal joint is created, and the input–output torque relationship is then studied. The different possible compliant embodiments based on the PRBM model were discussed and illustrated. Moreover, one of the proposed compliant counterparts is dimensioned as a power transmission coupling for a high misalignment angle, up to 45 deg. Further, a prototype was manufactured for the experimental evaluation, and it is shown that the results are consistent with the PRBM and the finite element model.

A compliant dual-axis gripper with integrated position and force sensing

This paper proposes a new flexure-based dual-axis gripper driven by two piezoelectric actuators (PEAs). For achieving two degree-of-freedom (2-DOF) micromanipulation in terms of grasping and rotating operation, the gripper is designed with an asymmetric structure which can be divided into left and right parts. Each part of the structure includes a two-stage amplification mechanism to accomplish displacement enlargement and motion transmission. Three groups of strain gages are integrated to measure the jaw displacements and the gripping force. To realize decoupling between the grasping and rotating function, the motion-guiding mechanisms of the two parts are elaborately designed with an orthogonal configuration. Analytical models of the gripper are derived using pseudo-rigid-body model (PRBM) method. Finite-element analysis (FEA) simulations are conducted to obtain the optimal geometric parameters and to evaluate the performance of the gripper. A close-loop position/force switching control strategy based on incremental PID algorithm is proposed to compensate the hysteretic nonlinearity of PEAs and guarantee precise and stable operation of the gripper. After that, a prototype gripper is developed and experimental investigations are conducted to verify the effectiveness of the gripper by executing a grasping-rotating-releasing operation of a metal wire. The experimental results indicate that the proposed gripper is capable of delicate and dexterous micromanipulation.

A large-range compliant remote center of motion stage with input/output decoupling

This paper presents the concept design of a large-range compliant remote center of motion (RCM) stage with input/output decoupling. The developed RCM stage can achieve 2-degree-of-freedom (2-DOF) rotation motion without generating extra lateral displacement in precision parallel alignment process. The RCM characteristic is realized based on parallelogram-based RCM module (PRM). The proposed stage is featured with input/output decoupling based on the novel designed structure. The input decoupling is realized by the employ of two up-down stacked arranged input stages. The output decoupling is realized by the orthogonal arrangement of two 1-DOF RCM stages combining the wire flexure hinges. The rectangular flexure hinge and the voice coil motor (VCM) are utilized to generate large-range rotation motion considering their large compliance and large stroke, respectively. The design, theoretical analysis and experimental test of the stage are presented. Based on pseudo-rigid-body-model (PRBM) method and compliance matrix method, the theoretical analysis is conducted to evaluate the kinematics, statics, dynamics and workspace of the RCM stage. Besides, finite element analysis (FEA) is conducted to validate the established models and an experimental system of the stage is set up for performance tests. The experimental results show that the proposed RCM stage can achieve a workspace of 14.4mrad×16.6mrad in its two working directions with a resolution of 15.1μrad. Moreover, the maximum coupling output angles about the two axes is less than 0.1mrad and 0.16mrad, which demonstrate the decoupling property of the developed stage.

Effect of initial curvature in uniform flexures on position accuracy

Position accuracy is a prerequisite for compliant mechanisms, especially in micro-scale applications. Generally, this feature depends on the flexures ability to imitate the revolute joints of the pseudo-rigid body model. In case of flexible elements, the center of the relative rotation varies its position during the deflections, affecting the position accuracy. In this paper, the role played by the initial curvature is investigated, in case of uniform primitive flexures. Analytical expressions are derived to evaluate the shift of the rotation axis with respect to the flexure centroid. An example shows the performance of four flexures with different curvatures, evaluated by comparing the rotation axis shift and the position error.

A statically balanced fully compliant power transmission mechanism between parallel rotational axes

This paper presents a fully compliant, potentially monolithic, power transmission mechanism which can rectify a large lateral offset between two parallel rotational axes. The planar nature of the design makes it ideal for manufacturing-limited applications such as micro/meso-scale power transmissions. The proposed compliant transmission is generated based on the Oldham Coupling and its equivalent Pseudo-Rigid-Body Model (PRBM). Normally, a compliant transmission mechanism cannot achieve a high efficiency due to the internal stiffness, i.e. actuation stiffness is not zero. However, in the proposed design, the internal stiffness is removed by static balancing and results in a statically balanced compliant transmission mechanism, i.e. with zero actuation stiffness. Therefore, the monolithic embodiment and static balancing features compensate for backlash, friction, assembly errors and poor mechanical efficiency inherent in conventional Oldham coupling, resulting in a transmission mechanism with high mechanical efficiency. Possible compliant design configurations based on the importance of different design criteria are discussed. Further, a compliant device based on the Paired Double Parallelogram (DP-DP) linear flexure bearing is designed and dimensioned. Moreover, the transmission stiffness, i.e. input-output rotational stiffness within the maximum allowable stress, and the actuation stiffness, i.e. minimum required actuation torque for certain angular displacement, of the designed device are predicted by the theoretical model and finite element modeling. Besides, the result shows the device is providing a constant transmission stiffness through a full cycle rotation. To prove the concept, a macro scale prototype is constructed and evaluated experimentally. It is shown that the results from the experiment are in agreement with the theoretical and finite element models.