Kinetostatic Model Research Articles

Modeling and Experimental Validation of a Compliant Underactuated Parallel Kinematic Manipulator

Parallel kinematic manipulators (PKMs) are increasingly used in a wide range of industrial applications due to the characteristics of high accuracy and compact structure. However, most of the existing PKMs are structured with heavy actuators and high stiffness. In this respect, this article proses a simple, yet effective, parallel manipulator that distinguishes itself through the following basis. First, underactuation: it employs only a single motor and a driving cable to actuate its three legs. Second, novel foot location: it uses a smart shape memory alloy clutch-based driving system (SCBDS), which catches/releases the driving cable, thus, making possible the robot underactuation. Finally, adjustable compliance: its double compliant joints on each limb with a stiffness-adjustable section, which renders a safe human–robotic interaction. To support and predict the performance of this underactuated compliant manipulator, a novel kinetostatic model was developed by considering the generalized internal loads (i.e., force and moment) in three compliant limbs and the external loads on the upper platform. Finally, based on the physical prototype, a set of experiments were conducted to validate the model proposed in this article. It was found that the proposed kinetostatic model can be validated with the average deviations of 1.8% in position and 2.8% in orientation, respectively. Furthermore, the workspace of the system (e.g., discrete and continuous workspace) was studied when different actuating strategies were employed, thus, emphasizing the advantages and the limitations of this novel system.

Kinetostatic and Dynamic Modeling of Flexure-Based Compliant Mechanisms: A Survey

Abstract Flexure-based compliant mechanisms are becoming increasingly promising in precision engineering, robotics, and other applications due to the excellent advantages of no friction, no backlash, no wear, and minimal requirement of assembly. Because compliant mechanisms have inherent coupling of kinematic-mechanical behaviors with large deflections and/or complex serial-parallel configurations, the kinetostatic and dynamic analyses are challenging in comparison to their rigid-body counterparts. To address these challenges, a variety of techniques have been reported in a growing stream of publications. This paper surveys and compares the conceptual ideas, key advances, and applicable scopes, and open problems of the state-of-the-art kinetostatic and dynamic modeling methods for compliant mechanisms in terms of small and large deflections. Future challenges are discussed and new opportunities for extended study are highlighted as well. The presented review provides a guide on how to select suitable modeling approaches for those engaged in the field of compliant mechanisms.

Kinetostatic modeling and characterization of compliant mechanisms containing flexible beams of variable effective length

Flexible beams of variable effective length, serve both transmission and actuation functionalities in compliant mechanisms, have been employed in many devices, e.g., thermal actuators and continuum robots. This difunctional feature is favorable when utilized for operations in confined space. However, the length variation introduces modeling difficulties, which poses a new challenge to designers. To accurate model flexible beams of variable effective length and characterize the behaviors of associated compliant mechanisms form the primary objectives of this study. The chained beam constraint model is revisited and extended to model beams of variable effective length. Modeling of a chevron shape thermal in-plane microactuator and a continuum mechanism are provided to demonstrate the effectiveness of the proposed method. The predicted results have a high degree of accuracy as compared to experimental results and nonlinear finite element results.

Design and Integration of a Parallel, Soft Robotic End-Effector for Extracorporeal Ultrasound.

In this work we address limitations in state-of-the-art ultrasound robots by designing and integrating a novel soft robotic system for ultrasound imaging. It employs the inherent qualities of soft fluidic actuators to establish safe, adaptable interaction between ultrasound probe and patient. We acquire clinical data to determine the movement ranges and force levels required in prenatal foetal ultrasound imaging and design the soft robotic end-effector accordingly. We verify its mechanical characteristics, derive and validate a kinetostatic model and demonstrate controllability and imaging capabilities on an ultrasound phantom. The soft robot exhibits the desired stiffness characteristics and is able to reach 100% of the required workspace when no external force is present, and 95% of the workspace when considering its compliance. The model can accurately predict the end-effector pose with a mean error of 1.18±0.29mm in position and 0.92±0.47° in orientation. The derived controller is, with an average position error of 0.39mm, able to track a target pose efficiently without and with externally applied loads. Ultrasound images acquired with the system are of equally good quality compared to a manual sonographer scan. The system is able to withstand loads commonly applied during foetal ultrasound scans and remains controllable with a motion range similar to manual scanning. The proposed soft robot presents a safe, cost-effective solution to offloading sonographers in day-to-day scanning routines. The design and modelling paradigms are greatly generalizable and particularly suitable for designing soft robots for physical interaction tasks.

A Fully Compliant Tristable Mechanism Employing Both Tensural and Compresural Segments

Abstract A multistable compliant mechanism is a device that can hold several distinct positions through the storage and release of the strain energy associated with deflections of the flexible members. This self-locking capability can benefit many applications such as threshold acceleration sensing, overload protection, and shape reconfiguration. This work presents a novel class of fully compliant tristable mechanisms called tensural–compresural tristable mechanisms (TCTMs), which forms three stable equilibrium positions through unique utilization of both tensural segments and compresural segments. To identify feasible designs, a kinetostatic model is developed using the chained beam-constraint-model (CBCM) for both tensural segments and compresural segments. Two TCTM designs accompanied with a prototype are presented to demonstrate the feasibility of this new tristable configuration and the effectiveness of the kinetostatic model.

Kinetostatic Modeling and Optimization of a Novel Horizontal-Displacement Compliant Mechanism

Abstract This paper presents kinetostatic modeling of a compliant mechanism for translational motion. This mechanism arranges all compliant members in an inverted way, which enables the robustness against beam buckling due to the heavy payload. To enable quick design and analysis of the mechanism, a nonlinear analytical model is then derived based on the chained beam constraint model, which is validated by nonlinear finite element simulation. Geometric parameter optimization is further carried out for desired motion characteristics. Finally, a prototype is fabricated and tested to verify the analytical model.

An energy-based approach for kinetostatic modeling of general compliant mechanisms

Kinetostatic analysis for general compliant mechanisms requires simultaneous considerations of kinematic and elasto-mechanical behaviors. Therefore, it will be difficult and low-efficiency to design and analyze general compliant mechanisms. In this paper, a kinetostatic modeling approach that integrates the screw theory with the energy method is proposed to provide an accurate and efficient solution. The coordinate transformations of stiffness and compliance matrices are deduced by using the screw theory. Then, the kinetostatic modeling of general compliant mechanisms is presented based on the energy method and the screw theory. The advantage of the proposed modeling approach is that there is no need to solve the laborsome equilibrium equations of nodal force when it is applied to the kinetostatic analysis of general compliant mechanisms. Performance comparisons of the proposed approach with the matrix displacement approach and the finite element analysis are respectively conducted for three exemplary mechanisms to reveal the prediction accuracy. The results indicate that the proposed modeling approach is applicable for fast performance evaluation of general compliant mechanisms at the early design stage.

Fast and Reliable Motion Model for Articulated Wheeled Mobile Robots on Extremely Rough and Rocky Terrains

Articulated wheeled mobile robots (AWMRs) have reconfigurable body structures that permit them to traverse rough terrains. Predicting trajectories of these robots on a rough surface is vital to carry out path planning. Several model-based approaches have been proposed in the past to predict these trajectories, but the existing work has been mostly focused on soft soil, or hard terrains with a smoothly changing surface. In the future, AWMRs would likely be sent to challenging scenarios that are rocky. Hence, a novel model for AWMRs has been proposed that extends existing Kineto-static motion models to consider multiple points of contacts for each of the wheels of the robot, which is vital for rocky terrains. Simulations are carried out based upon the COLE VII robot to compare the proposed method with state-of-the-art Kineto-static and differential algebraic equation based constraint dynamics models. The accuracy of these techniques and the proposed method is benchmarked against the popular open dynamics engine. Two-way analysis of variance is performed and it is shown that accounting for wheel width and multiple points of contact does not have a significant impact on the simulation results on smoothly undulating terrain, whereas, it does on a rocky terrain. Moreover, accounting for wheel width and multiple points of contact does not significantly impact the run time of the underlying dynamics algorithm for fast collision checking.

On the Equivalent Position Workspace for a Coal Gangue Picking Robot

Coal gangue separation is of key important for green mining. Robotic separation of coal and gangue based on the machine vision system, which is called a coal gangue picking robot with a gangue grab driven by four cables, is developed in this study. Here, this paper focuses on the equivalent position workspace, within which a coal gangue picking robot possesses the identical stability, to find out any more information about the structural stability for a coal gangue picking robot. First, the kinematic and kinetostatic models of the coal gangue picking robot are presented for analyzing the effects of it on the structural stability for the coal gangue picking robot. And moreover, a non-iterative polynomial-based optimization algorithm with the proper optimal objective function is presented based on the convex optimization theory, in which the cable with the minimum cable tension at any pose is determined. Then, three position performance indices are proposed to show the important effects on the structural stability for the coal gangue picking robot in a specified region of the workspace. Besides, a new workspace, the Equivalent Position Workspace (EPW), is introduced. Finally, the theoretical relationship between the two performance indices and the stability is corrected based on simulation results. The research has important guiding significance and practical value for coal gangue robotic separation.

On Generating Expected Kinetostatic Nonlinear Stiffness Characteristics by the Kinematic Limb-Singularity of a Crank-Slider Linkage with Springs

Being different from avoidance of singularity of closed-loop linkages, this paper employs the kinematic singularity to construct compliant mechanisms with expected nonlinear stiffness characteristics to enrich the methods of compliant mechanisms synthesis. The theory for generating kinetostatic nonlinear stiffness characteristic by the kinematic limb-singularity of a crank-slider linkage is developed. Based on the principle of virtual work, the kinetostatic model of the crank-linkage with springs is established. The influences of spring stiffness on the toque-position angle relation are analyzed. It indicates that corresponding spring stiffness may generate one of four types of nonlinear stiffness characteristics including the bi-stable, local negative-stiffness, zero-stiffness or positive-stiffness when the mechanism works around the kinematic limb-singularity position. Thus the compliant mechanism with an expected stiffness characteristic can be constructed by employing the pseudo rigid-body model of the mechanism whose joints or links are replaced by corresponding flexures. Finally, a tri-symmetrical constant-torque compliant mechanism is fabricated, where the curve of torque-position angle is obtained by an experimental testing. The measurement indicates that the compliant mechanism can generate a nearly constant-torque zone.

The design and kinetostatic modeling of 3PPR planar compliant parallel mechanism based on compliance matrix method.

Compliant Parallel Mechanisms (CPMs) are widely used in micro/nano-positioning systems. In recent years, CPMs with a large travel range (≥1 mm) have been getting increasing attention. In this paper, a 3 Prismatic-Prismatic-Revolute (3PPR) planar CPM with a motion range of 5 mm × 5 mm × 5° is designed. The mechanical structure is characterized by the application of three joints based on a compliant four-bar mechanism, which guarantees the motions along/about the specific axes to improve motion accuracy. A double blade rotary pivot is served as a revolute joint to decrease the drift of pivot and produce a large rotation range without loss of compactness. The compliance matrix method is implemented to kinetostatic modeling, and the input coupling effect, which is always neglected or modeled complicatedly in 3-Degree-of-Freedom planar CPMs, is involved with the principle of superposition. The feasibility of the mechanical design and the accuracy of the developed kinetostatic model are validated by finite element analysis and experiments, respectively. The results indicate that the modeling method based on the compliance matrix method is concise, effective, and accurate, and can be extended to other more complicated CPMs.

Influence of non-ideal fixed-end constraints on kinetostatic behaviors of compliant bistable mechanisms

Bistable mechanisms can maintain two distinct positions without energy consumption, which made them widely used in many special situations. The performance of bistable mechanisms may suffer from its non-ideal fixed-end constraints (the deformation of its ostensibly rigid frame), which may even incapacitate the bistability of the mechanisms. To capture the influence of non-ideal constraints on the behaviors of the mechanisms, a kinetostatic model for bistable mechanisms is presented in this paper. In the model, behaviors of both the frame and flexible beams are considered and characterized using the Chained Beam Constraint Model (CBCM). Three examples are modeled and analyzed to show the effectiveness of the model for evaluating the influence of non-ideal constraints on the behaviors of the mechanisms. The results are validated by the results of finite element analysis as well as experiments.

Conceptual design and kinetostatic analysis of a modular parallel kinematic machine-based hybrid machine tool for large aeronautic components

Abstract Precision manufacturing and intelligent assembly in the aeronautic industry pose new challenges for the design of Flexible Manufacturing Systems (FMSs). To address these issues, a modular Parallel Kinematic Machine (PKM)-based hybrid machine tool is proposed. The 5-axis hybrid machine tool is conceptually designed by integrating 3-Degree-Of-Freedom (DOF) over-constrained PKMs with a 2-DOF serial mechanism including a unique double-circumferential guideway. By integrating accessory devices, the proposed machine provides a promising alternative solution to building a novel FMS for the flexible manufacturing requirements of larger arc-shaped aeronautic components. A kinematic model is established to conduct an inverse kinematic analysis to predict the reachable workspace by using a ‘sliced partition’ searching algorithm. To evaluate the kinetostatic performance of the hybrid machine tool, a modified kinetostatic model is established by including the compliances of all joints and limb structures. The prediction accuracy of the proposed kinetostatic model is validated by numerical simulations. Two kinetostatic performance indexes, the average reaction index and the average displacement index, are formulated and applied to reveal the gravity-caused joint reactions and elastic displacement of the hybrid machine tool, respectively. The analyses show that the kinetostatic performances of the machine are heavily affected by gravity; thus, gravity must be considered during the early design stage. Notably, with minor revisions, the proposed kinetostatic model and performance indexes can be applied to other hybrid mechanical systems to efficiently evaluate their kinetostatic performances.

A general two-port dynamic stiffness model and static/dynamic comparison for three bridge-type flexure displacement amplifiers

Abstract Bridge-type compliant mechanisms (BTCM) are frequently used as displacement amplifiers in the precision manipulation. There have been a considerable number of studies on the kinetostatic modeling and analysis of BTCM in the past decade but less on the dynamics or finding optimal geometric parameters in terms of both kinetostatics and dynamics. To this end, this paper presents a two-port dynamic stiffness model to describe the simultaneous kinetostatics and dynamics of three popular bridge-type compliant mechanisms from the perspective of input and output ports. The displacement amplification ratio, input/output stiffness, natural frequencies and dynamic response of these three BTCM can be efficiently and accurately solved just by changing geometric parameters with the same model. With the two-port dynamic stiffness model, the dynamic modeling of BTCM is simplified as a statics-similar problem differing from the ubiquitous Lagrange-based dynamic methods in previous studies. Of particular interest for model application is to exploit the optimal geometric parameters in each BTCM and then compare the three BTCM in terms of kinetostatics and dynamics to provide quantitative insight for designers. At last, several design criteria for these BTCM are summarized and recommended based on the parameter influence analysis. In particular, the rhombic amplifier has higher dynamic frequency and smaller input stiffness under the same output displacement, while the parallel and aligned amplifiers have larger output stiffness which is benefit for providing larger output force.

Kinetostatic Modeling of Bridge-Type Amplifiers Based on Timoshenko Beam Constraint Model

In this paper, we develop an accurate kinetostatic modeling method for bridge-type amplifiers by incorporating the impacts of nonlinear shear effect, center-shifting and load-stiffening. To account for the nonlinear stress-stiffening and shear effects, a Timoshenko Beam Constraint Model (TBCM) is first investigated to accurately predict the deformations of the short beam flexure hinges popularly employed in the bridge-type amplifiers. Accordingly, a flexible branched chain model is established for bridge-type amplifiers, where the input and output displacements, as well as the displacement amplification ratio and the input stiffness, are derived. The results indicate significant nonlinearities of the amplification ratio and the input stiffness with respect to the driving forces, which are further verified by the finite element analysis (FEA) results. The proposed modeling method can derive a more accurate model of the bridgetype amplification mechanism to capture its kinetostatic behaviors, which can better support the design and control of flexure mechanism based nano-manipulating systems.

A general approach for generating kinetostatic models for planar flexure-based compliant mechanisms using matrix representation

Kinetostatic modeling of a flexure-based compliant mechanism (FCM) is always a complicated and error-prone process because it involves not only the formulation of the geometric compatibility but also the formulation of the load equilibrium of the mechanism. In this paper, we propose a general approach for automatically generating kinetostatic models for FCMs based on their matrix representation. The approach utilizes virtual flexure hinges, link-flexure incidence matrices and path matrices to unify and simplify the formulation of the kinetostatic equations of FCMs. Four case studies are provided to demonstrate the use of the proposed method for modeling various FCMs.

Design and kinetostatic modeling of a compliant gripper for grasp and autonomous release of objects

ABSTRACTA gripper with an embedded compliant bistable mechanism (BM) for gripping and autonomous release of objects is developed. Due to adhesion forces, objects might stick to the end effector of a gripper upon release, where a shaking operation may be employed to release the objects. Vibration of the end effector induced by an impact pestle adjacent to the shuttle mass of the BM may achieve autonomous release of objects adhered to the end effector. Gripping and autonomous release of objects are accomplished when the BM moves between its two stable equilibrium positions. An analytical model is developed to predict the kinetostatic behavior of the BM and to assist in the design of the gripper.

Three dimensional force estimation for steerable catheters through bi-point tracking

Contact forces play a significant role in the success of cardiac ablation. However, it is still challenging to estimate the applied contact force during the intervention when a catheter is under large bending or experiences multiple contact points along its body. A multi-element kinetostatic model of a tendon-driven catheter is proposed for real-time intrinsic force sensing. The model is able to accurately predict the steerable section shape of the catheter for given tendon tensions as well as the contact force at any known location on the steerable section. An algorithm is proposed which estimates the contact force on the steerable section using the model-based shape prediction in combination with end-position tracking of the steerable section. In this paper, undefined parameters and contact states of the force and shape estimation are defined and investigated. The shape prediction is validated in 3D space. The contact force estimation is validated with different catheter shpae, contraint catheter and buckling. It can be seen that end-position of the steerable section can be predicted with an accuracy of about 2.3 mm. In the validations, the 3-dimensional contact forces can be estimated accurately with an error of about 0.018 N and 1.6 ms computation time. Furthermore, the contact force estimation algorithm are able to incorporate external physical constraints along the catheter, which is validated in an experimental setup.

Development and analysis of a bridge-lever-type displacement amplifier based on hybrid flexure hinges

Bridge-type mechanism is one of the most widely used displacement amplifiers in micro scale applications due to its compact and symmetrical structure. However, a drawback of the bridge-type mechanism that restricts its further applications is the limited amplification ratio. To solve this problem, a bridge-lever-type displacement amplifier is developed and analyzed in this paper. Compared with the conventional design, the proposed amplifier not only maintains a compact and symmetrical structure, but also features a high amplification ratio and high load capacity. To reduce the displacement loss of the amplifier and enhance its load capacity, the hybrid flexure hinges are employed in the novel design. Furthermore, the kineto-static model based on the compliance matrix method and the dynamic model based on Lagrangian method are established to analyze the bridge-lever-type amplifier. Finally, a prototype is fabricated whose amplification ratio is approximately 48 and 34 in the case of zero load and 30 N load respectively, which is confirmed by FEA simulation and experimental study.

Kinetostatic modeling of complex compliant mechanisms with serial-parallel substructures: A semi-analytical matrix displacement method

Kinetostatic analysis of compliant mechanisms are crucial at the early stage of design, and it can be difficult and laborsome for complex configurations with distributed compliance. In this paper, a kinetostatic modeling method for flexure-hinge-based compliant mechanisms with hybrid serial-parallel substructures is presented to provide accurate and concise solutions by combining the matrix displacement method with the transfer matrix method. The transition between the elemental stiffness matrix and the transfer matrix of flexure hinges/flexible beams is straightforward, enabling the condensation of a hybrid serial-parallel substructure into one equivalent two-node element simple. A general kinetostatic model of the whole compliant mechanisms is first established based on the equilibrium equation of the nodal force. Then, a condensed two-port mechanical network representing the input/output force-displacement relations of single-degree-of-freedom (DOF) compliant mechanisms and the Jacobian matrix for multi-DOF compliant mechanisms are respectively built. Comparison of the proposed method with the compliance matrix method in previous literature, finite element analysis and experiment for three exemplary mechanisms reveals good prediction accuracy, suggesting its feasibility for fast performance evaluation and parameter optimization at the initial stage of design.