Kinetostatic Model Research Articles

Design and nonlinear spatial analysis of compliant anti-buckling universal joints

Compliant universal joints have been widely used in many applications such as precision transmission mechanisms and continuum robots. However, their nonlinear spatial analysis in terms of load-displacement relations is less investigated in the compliant mechanisms community, which are needed to show the physical insight into constraint behavior of the universal joint. In addition, the design of existing compliant universal joints is not robust to withstand buckling under applied compression loads. This paper aims to address these problems and starts from presenting a novel anti-buckling universal joint consisting of two inversion-based symmetric cross-spring pivots (IS-CSPs). Two nonlinear spatial models of the IS-CSP and of anti-buckling universal joint are proposed, resorting to two single-sheet closed-form kinetostatic models as the first step, respectively. Then center shifts, primary rotations, and load-dependent stiffness are parametrically studied under different loading conditions over a load and displacement range of practical interest, namely, point loads, cable-force actuations, and varying loading positions. The modeling results of these performance characteristics are shown to be accurate using nonlinear finite element analysis. In addition, preliminary experimental tests are carried out to investigate the manufacturability of the prototype and verify the nonlinear spatial models. Finally, this paper presents and models two new bi-directional anti-buckling universal joints, each with two IS-CSPs and two non-inversion-based symmetric cross-spring pivots (NIS-CSPs).

Application of computer systems for modeling dynamic processes of lifting machines

The main task of mechanical engineering is to organize the production of a range of machines to meet the needs of all industries. These are power, transport, lifting and transport units, agricultural machinery, construction industry, etc. Among them, one can single out devices in which the relative movement of their parts is assigned, that is, kinematic pairs are included in the calculation models. The real operating conditions of machines are varied, but most often they are associated with periodic starts-stops, which determines the relevance of the study of unsteady modes. The analysis of the operation of such models becomes more complicated. For successful design results, mathematical modeling of individual processes in mechanisms is carried out. One of the first calculations is dynamic. Modern, available CAD / CAE systems for modeling and analysis provide automation capabilities, building more realistic design models. The paper discusses the approbation of the use of CAD for modeling the dynamics of a jib crane with a set of four units: platform, boom, sleeve and rod. The developed model is combined: the platform and the sleeve correspond to the kinetostatic model, and the boom and rod are elastic. The crane is designed to perform lifting operations in a vertical plane, with the possibility of relative movement in 3 rotational and one translational kinematic pairs. The performed calculations of the static, modal and dynamic analyzes of the links of the mechanism confirm the adequacy of their models. Among them is the task of instantaneous load application, which is typical for the "lifting and picking" operating mode of crane lifting mechanisms. The deformation of the entire structure in one of the boom positions is also considered. The determination of the reaction forces in the hydraulic cylinder provides important information for the selection of the power unit.

A flexure-based displacement reducer capable of achieving very large reduction ratio

To achieve positioning of nanometer or even sub-nanometer resolution from traditional piezoelectric actuators and giant magnetostrictive actuators, a bridge-type differential displacement reducer, which shows the capability of obtaining very large reduction ratio, is proposed. The reducer contains two bridge-type flexure mechanisms connected in a way that the output of the reducer equals the difference of the outputs of the two mechanisms. If the two bridge-type flexure mechanisms are identical, no matter how large the input is, the output will always be 0, indicating an infinite reduction ratio theoretically. Therefore, introducing a slight difference between the two mechanisms can yield a very large reduction ratio. A kinetostatic model for the reducer is developed, base on which a reducer exhibiting a reduction ratio of 100 is designed and prototyped. The results of the kinetostatic model, the finite element model and the experiment agree well with each other, validating the effectiveness of the proposed reducer and the correctness of the kinetostatic model.

Nonlinear kinetostatic modeling and analysis of a large range 3-PPR planar compliant parallel mechanism

Kinetostatic modeling is critical in the design of large range multi-degree-of-freedom compliant parallel mechanisms. However, geometric nonlinearities and coupling effects between kinematic chains create difficulties to the modeling. This paper presents a nonlinear method of kinetostatic modeling for these mechanisms. Geometric nonlinearities are considered by applying the beam constraint model, and load equilibrium conditions and geometric compatibility equations are combined to formulate the coupling effects between kinematic chains. Based on the proposed method, an iterative nonlinear kinetostatic model is developed for a 3-prismatic–prismatic–revolute large range compliant parallel mechanism. Approximate analytical models for three flexure joints are adopted to avoid the nested iteration algorithm, thereby increasing the computational efficiency. Compared with the linear kinetostatic model, the actuation forces are almost identical, and the open-loop position errors decrease by 68% to a value of 32.5 μm for a circular trajectory with a radius of 2.5 mm using finite element analyses. Furthermore, the computational efficiency increases significantly compared with the nested iterative model. In addition, the kinetostatic characteristics of the mechanism are analyzed, and the main reasons for geometric nonlinearities are investigated. Finally, experiments are conducted to validate the developed iterative nonlinear kinetostatic model.

A non-transit fully compliant tristable mechanism capable of direct switching between every two stable positions

A tristable compliant mechanism is a mechanical device that can hold three distinct positions where the strain energy stored in the flexible members falls in its minima. This unique feature makes them very useful in many applications such as overload protection, threshold acceleration sensing, and shape reconfiguration. For the currently available tristable designs, there is a middle stable position among the three stable positions, and switching between the other two stable positions requires to pass through the middle one. This work presents a novel fully compliant tristable mechanism called non-transit tristable mechanism (NTTM), which can directly switch between every two stable positions without passing through the other one. A kinetostatic model using the chained beam-constraint-model is developed for the proposed mechanism, based on which two NTTMs are successfully identified. The non-transit tristable behaviors of the NTTM designs are verified by the results of nonlinear finite element model and the experimental results of a 3D printed prototype.

Design and modeling of a compact compliant stroke amplification mechanism with completely distributed compliance for ground-mounted actuators

This paper proposes a new compliant mechanism for the stroke amplification of piezoelectric actuators. Compared with the existing ones, this compliant stroke amplification mechanism (CSAM) has several advantages including lightweight, less stress concentration, large motion range, as well as ease of manufacture in macro- and micro-scales, mainly due to the completely distributed compliance and largely reduced moving mass. Kinetostatic models of the CSAM, with consideration of the payloads applied on the output stage, are derived for quick and insightful determinate analysis, which enables optimization of the associated parameters to achieve different objectives. The results obtained from the kinetostatic models are in reasonable agreement with the FEA simulation results, with less than 3.8% difference when the input displacement is less than 10 µm. An optimization method, based on the analytical models, is introduced and employed to increase the amplification ratio of the CSAM by up to 240%. The optimized CSAM is an excellent candidate for the stroke amplification of piezoelectric actuators, which is fabricated and experimentally tested. The optimization method is able to be extended to design other compliant mechanisms with optimized size, shape and topology configuration simultaneously.

A compliant guiding mechanism utilizing orthogonally oriented flexures with enhanced stiffness in degrees-of-constraint

The large stroke is usually realized by lowering stiffness along the degrees of freedom, which usually leads to a decrease of stiffness along the degrees of constraint. A high stiffness ratio is crucial for reducing the deflections induced by disturbances such as eccentric force and the gravity of the load. Besides, the fatigue life of these mechanisms will be shortened due to the large stress caused by the large deflection. This paper proposed a new guiding mechanism using orthogonally oriented flexures to improve the stiffness along the degrees of constraint and reduce stress concentration. The energy method is utilized to obtain the kinetostatic model of the guiding mechanism by taking the nonlinear deflection into account, based on which the mechanism is optimized by simultaneously considering the topology and size. As compared to the performance of traditional design obtained through the same optimization objective and constraints, the optimal design effectively improves the stiffness along the degrees of constraint, whose accuracy is also validated by the finite element analysis results. Experimental results show that the proposed mechanism increases the stiffness ratio Kaz/Kx by 3.54 times compared to the traditional mechanism.

Kinetostatic Modeling of Planar Compliant Mechanisms With Flexible Beams, Linear Sliders, Multinary Rigid Links, and Multiple Loops

Abstract This paper presents kinetostatic models of planar compliant mechanisms with multinary rigid links, multinary joints, sliders, and multiple loops based on the chained beam constraint model. The focus is on modeling of several building blocks of the beam type compliant mechanisms to aid in their design. The modeling approaches are based on the loop-closure equations and the static equilibrium conditions. Models of the multinary rigid links, multinary joints, and sliders are presented. As a result, the kinetostatic models of the compliant mechanisms can be systematically formulated by using these building blocks. Several mechanisms constructed by the building blocks are modeled and verified by finite element analyses. A case study is provided to demonstrate the application of the developed models. These models pave the way for versatile applications of the chained beam constraint model for the design and analysis of beam type planar compliant mechanisms.

Kinetostatic Modeling of Dual-Drive H-Type Gantry With Exchangeable Flexure Joints

Abstract The flexure joints are proposed to replace the rigid assembly between the cross-arm and the moving carriages of dual-drive H-type gantry (DHG) for higher reliability and fine rotational alignments. In the literature, the flexure joint of the DHG is modeled as an ideal linear torsional spring, resulting in an inaccurate estimation of the cross-arm’s angle. In this study, a generalized analytical kinetostatic model of flexure-linked DHG is built by considering the geometric nonlinearities. The expressions of beam coefficients in the model are obtained from either beam constraint model (BCM) or Timoshenko BCM (TBCM) according to the given criterion of length-to-thickness ratio. The model is capable to accurately estimate any two variables among the rotation angle of the cross-arm, the misalignment of two carriages, and the net driving force, as long as the other is known. Simulations and experiments on the testbed validate the accuracy and show practical appeals of the proposed model.

Fully compliant bistable mechanisms with enhanced pitch stiffness

For compliant bistable mechanisms with planar configurations and exhibiting two in-plane stable states, their flexible beams are supposed to undergo in-plane bending deflections, but the out-of-plane deflections can significantly influence the kinetostatics of the mechanism, resulting in inconsistent bistable behaviors when off-axis or eccentric loads present. In this paper, we propose a novel bistable mechanism utilizing torsion-stiffness enhanced flexible beams to restrain the shuttle from out-of-plane rotation. An analytical kinetostatic model is developed for the proposed bistable mechanism. Five bistable examples are presented to demonstrate the effectiveness of the proposed bistable mechanism in suppressing unwanted motions and the correctness of the proposed kinetostatic model. The results show that the novel bistable designs are much stiffer along the out-of-plane rotation thus are more robust against off-axis or eccentric loading condition, especially when the shuttle is displaced to a position around the second equilibrium stable position (where the flexible beams are in the post-buckling states).

An Energy-Based Framework for Nonlinear Kinetostatic Modeling of Compliant Mechanisms Utilizing Beam Flexures

Abstract Although energy-based methods have advantages over the Newtonian methods for kinetostatic modeling, the geometric nonlinearities inherent in deflections of compliant mechanisms preclude most of the energy-based theorems. Castigliano's first theorem and the Crotti-Engesser theorem, which don't require the problem being solved to be linear, are selected to construct the energy-based kinetostatic modeling framework for compliant mechanisms in this work. Utilization of these two theorems requires explicitly formulating the strain energy in terms of deflections and the complementary strain energy in terms of loads, which are derived based on the beam constraint model. The kinetostatic modeling of two compliant mechanisms are provided to demonstrate the effectiveness of the explicit formulations in this framework derived from Castigliano's first theorem and the Crotti-Engesser theorem.

Design and Analysis of a Novel Flexure-Based Dynamically Tunable Nanopositioner.

Various tools, such as biomedical manipulators, optical aligners, and ultraprecision manufacturing tools, implement nanopositioners that must be dynamically tunable to satisfy the requirements of different working conditions. In this paper, we present the design and analysis of a flexure-based nanopositioner with dynamically tunable characteristics for the implementation of a high-performance servomechanism. The nanopositioner is composed of four flexure beams that are positioned in parallel and symmetric configurations sandwiched between magnetorheological elastomers (MREs). The properties of MREs impart dynamicity to the nanopositioner, allowing the workspace, stiffness, and damping characteristics in particular to be tuned under the action of an external magnetic field. By utilizing elastic beam theory and electromagnetic field coupling analysis, kinetostatic and dynamic models of the proposed nanopositioner were established to predict the variable stiffness property and dynamically tunable characteristics. The models were validated by performing a finite element analysis. Herein, it is shown that the proposed nanopositioner model can actively adjust the trade-offs between the working range, speed, and sustained load capability by changing the magnetic field. The proposed dynamic tuning method offers new insight into the design of flexure-based nanopositioners for real applications.

Chebyshev inclusion function based interval kinetostatic modeling and parameter sensitivity analysis for Exechon-like parallel kinematic machines with parameter uncertainties

This paper aims to investigate the effects of parameter uncertainties on kinetostatic behaviors of Exechon-like parallel kinematic machines (PKMs). A general interval kinetostatic model for Exechon-like PKMs is established by using Chebyshev inclusion function. The prediction accuracy and efficiency of the interval model are numerically verified. Based on the interval model, two indexes are formulated to quantify the effects of parameter uncertainties on kinetostatics of the PKM. The gravity-caused elastic displacements of the PKM are computed throughout its workspace when considering design parameters as interval variables. A sensitivity analysis is carried out to identify the most influential design variables when the PKM is under a condition of parameter uncertainties. Based on this, a cost-effective scheme of tolerance allocation is designed for the PKM in a convenient manner. The analyses reveal the interval kinetostatic response of the PKM is strongly position-dependent and nonlinear-related to multiple uncertain parameters. Hence, parameter uncertainties need to be fully considered during early design stage of such PKMs. The proposed interval model can be further applied to similar over-constrained parallel robots with minor modifications.

Synthesis and modelling of one rotational constraint orientated compliant mechanisms

This paper proposes dozens of One Rotational Constraint orientated Compliant Mechanisms (ORCCMs), mainly utilizing a newly proposed virtual rigid-body mechanism based replacement method and the existing positon space method. These ORCCMs have four types of configurations, including basic, transformed, parallel and serial configurations. The basic ORCCM has the simplest geometrical structure that forms the constituent component of the other configurations. Parametric kinetostatic (linear) models of these ORCCMs are derived for quick and insightful determinate synthesis/analysis toward optimization of the associated parameters to achieve the intended objectives, which can also promote further nonlinear modelling. The linear analytical results are in reasonable agreement with the FEA simulation results, over an approximate displacement range of ±10% of beam length for translations or ±0.08 rad for rotations. Some of the derived analytical models are also verified through experimental tests on one fabricated prototype of the parallel ORCCMs. The proposed ORCCMs along with the well-known slender wire beams play an important role on the synthesis of multi-DOF kinematic decoupled compliant mechanisms and the design of other instruments and robots such as continuum robots.

Kinetostatic analysis of 6-DOF compliant platform with a multi-stage condensed modeling method

Matrix displacement method, based on matrix operation without complex internal force analysis, gives accurate solutions and concise process for the kinetostatic analysis of the compliant mechanisms. However, there are some problems of tedious node numbering in the general matrix displacement method. In this paper, a multi-stage condensed modeling method is proposed to establish kinetostatic model for the compliant platform with complex configurations. Based on the matrix displacement method in structural mechanics and combining with the transfer matrix and coordinate transformation, the complex series–parallel configuration is subjected to multi-stage stiffness equivalent to obtain a concise input/output two-port mechanical network. Then, the proposed method is used to analyze the kinetostatic of the 6-degree-of-freedom (DOF) compliant platform. And a good prediction accuracy is shown by comparison with finite element analysis and experiment. Moreover, the results also show that the hinge thickness and the hinge spacing at the maximum amplification ratio of the bottom platform satisfies the linear condition, which provides implications for the design and optimization of the compliant mechanisms based on the bridge-type amplifiers.

Modeling, Calibration, and Evaluation of a Tendon-Actuated Planar Parallel Continuum Robot

In this work, a novel planar parallel continuum robot (PCR) is introduced, consisting of three kinematic chains that are coupled at a triangular end-effector platform and include tendon-actuated continuum segments. The kinematics of the resulting structure are derived by adapting the descriptions for conventional planar parallel manipulators to include constant curvature bending of the utilized continuous segments. To account for friction and non-linear material effects, a data-driven model is used to relate tendon displacements and curvature of the utilized continuum segments. A calibration of the derived kinematic model is conducted to specifically represent the constructed prototype. This includes the calibration of geometric parameters for each kinematic chain and for the end-effector platform. During evaluation, positioning repeatability of 1.0% in relation to one continuum segment length of the robot, and positioning accuracy of 1.4%, are achieved. These results are comparable to commonly used kineto-static modeling approaches for PCR. The presented model achieves high path accuracies regarding the robot's end-effector pose in an open-loop control scenario.

Design and modeling of a compliant gripper with parallel movement of jaws

A compliant gripper with parallel movement of jaws is developed. The gripper is composed of a bar linkage mechanism and a bistable mechanism. After a target object is grasped, the embedded bistable mechanism can maintain the gripping of the object with no energy consumption. Unstable fixation due to rotary motion of opposing gripping arms of traditional tweezer-like grippers is alleviated by the proposed gripper. Kinetostatic models of the device based on chained beam constraint model are derived to assist the design of the device. Grasp function of an object is accomplished while the gripper proceeds from its first stable equilibrium position to its second stable equilibrium position, and release of the object is achieved when the gripper returns back to its first stable equilibrium position.

Modeling and analysis of soft robotic fingers using the fin ray effect

Soft grasping of random objects in unstructured environments has been a research topic of predilection both in academia and in industry because of its complexity but great practical relevance. However, accurate modeling of soft hands and fingers has proven a difficult challenge to tackle. Focusing on this issue, this article presents a detailed mathematical modeling and performance analysis of parallel grippers equipped with soft fingers taking advantage of the fin ray effect (FRE). The FRE, based on biomimetic principles, is most commonly found in the design of grasping soft fingers, but despite their popularity, finding a convenient model to assess the grasp capabilities of these fingers is challenging. This article aims at solving this issue by providing an analytic tool to better understand and ultimately design this type of soft fingers. First, a kinetostatic model of a general multi-crossbeam finger is established. This model will allow for a fast yet accurate estimation of the contact forces generated when the fingers grasp an arbitrarily shaped object. The obtained mathematical model will be subsequently validated by numerically to ensure the estimations of the overall grasp strength and individual contact forces are indeed accurate. Physical experiments conducted with 3D-printed fingers of the most common architecture of FRE fingers will also be presented and shown to support the proposed model. Finally, the impact of the relative stiffness between different areas of the fingers will be evaluated to provide insight into further refinement and optimization of these fingers.

Large-Stroke Constant-Force Mechanisms Utilizing Second Buckling Mode of Flexible Beams: Evaluation Metrics and Design Approach

AbstractCompliant constant-force mechanisms (CCFMs), which provide a near constant-force output over a range of displacement, can benefit many applications. This work proposes a novel large-stroke CCFM (abbreviated as B2CCFM) that utilizes the second buckling mode of flexible beams. Two general nondimensionalized metrics, one describing the variation of output force and the other describing the operational displacement, are proposed to effectively characterize the performances of various CCFMs. Based on the general metrics, design formulas that can help designers quickly find suitable B2CCFM design for a specific application are obtained. A kinetostatic model for B2CCFM is also provided based on the chained beam constrain model to verify B2CCFM designs. An example accompanied with a prototype is presented to verify this novel CCFM and the effectiveness of the design formulas. The experimental results show that the B2CCFM example outputs a constant-force in a range as large as 45% of the beam length with variation less than 4.7%. The nondimensionalized metrics were demonstrated in comparison of several CCFMs, and the comparison results show the superior performances of B2CCFMs.

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.