General Kinetostatic Modeling and Deformation Analysis of a Two-Module Rod-Driven Continuum Robot with Friction Considered

Continuum robots actuated by flexible rods have large potential applications,such as detection and operation tasks in confined environments,since the push and pull actuation of flexible rods withstand tension and compressive force,and increase the structure's rigidity.In this paper,a generalized kinetostatics model for multi-module and multi-segment continuum robots considering the effect of friction based on the Cosserat rod theory is established.Then,the model is applied to a two-module rod-driven continuum robot with winding ropes to analyze its deformation and load characteristics.Four different in-plane configurations under the external load term as S1,S2,C1,and C2 are defined.Taking a bending plane as an example,the tip deformation along thex-axis of these shapes is simulated and compared,which shows that the load capacity of C1 and C2 is generally larger than that of S1 and S2.Furthermore,the deformation experiments and simulations show that the maximum error ratio without external loads relative to the total length is no more than 3%,and it is no more than 4.7%under the external load.The established kinetostatics model is proven sufficient to accurately analyze the rod-driven continuum robot with the consideration of internal friction.

Gravity-Based Kinetostatic Modeling of Parallel Manipulators Using Screw Theory

The pose accuracy of parallel manipulators(PMs)is a key index to measure their performance.Establishing the grav-ity-based kinetostatic model of a parallel robot provides an important basis for its error composition and accuracy improvement.In this paper,a kinetostatic modeling approach that takes real gravity distribution into consideration is proposed to analyze the influence of gravity on the infinitesimal twist and actuator forces of PMs.First,the duality of the twist screw and constraint wrenches are used to derive the gravity-attached constraint wrenches independent of the external load and the limb stiffness matrix corresponding to the kinematics-based constraint wrenches.Sec-ond,the gravity model of the mechanism is established based on the screw theory and the principle of virtual work.Finally,the analytical formulas of the infinitesimal twist and the actuator force of PMs are obtained,and the influences of the external load,platform gravity,and rod gravity on the stiffness of the mechanism are decoupled.The non-overconstrained 3RPS and overconstrained 2PRU-UPR PMs are taken as examples to verify the proposed method.This research proposes a methodology to analyze the infinitesimal deformation of the mechanism under the influence of gravity.

Kinetostatic Modeling and Analysis of an Exechon Parallel Kinematic Machine(PKM) Module

As a newly invented parallel kinematic machine（PKM）, Exechon has found its potential application in machining and assembling industries due to high rigidity and high dynamics. To guarantee the overall performance, the loading conditions and deflections of the key components must be revealed to provide basic mechanic data for component design. For this purpose, a kinetostatic model is proposed with substructure synthesis technique. The Exechon is divided into a platform subsystem, a fixed base subsystem and three limb subsystems according to its structure. By modeling the limb assemblage as a spatial beam constrained by two sets of lumped virtual springs representing the compliances of revolute joint, universal joint and spherical joint, the equilibrium equations of limb subsystems are derived with finite element method（FEM）. The equilibrium equations of the platform are derived with Newton＇s 2nd law. By introducing deformation compatibility conditions between the platform and limb, the governing equilibrium equations of the system are derived to formulate an analytical expression for system＇s deflections. The platform＇s elastic displacements and joint reactions caused by the gravity are investigated to show a strong position-dependency and axis-symmetry due to its kinematic and structure features. The proposed kinetostatic model is a trade-off between the accuracy of FEM and concision of analytical method, thus can predict the kinetostatics throughout the workspace in a quick and succinct manner. The proposed modeling methodology and kinetostatic analysis can be further expanded to other PKMs with necessary modifications, providing useful information for kinematic calibration as well as component strength calculations.

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.

Effect of Degree-of-Symmetry on Kinetostatic Characteristics of Flexure Mechanisms:A Comparative Case Study

The current research of kinetostatic characteristics in flexure mechanisms mainly focus on the improvement of accuracy. To reduce or eliminate the parasitic motion is considered as an approach by using the common knowledge of symmetry. However, there is no study on designing the flexure mechanisms with symmetrical features as many as possible for better kinetostatic performance, when considering the resulting cost by the symmetry. In this paper, the concept of degree of symmetry(DoS) is proposed for the first time, which is committed to symmetry design in the phase of conceptual design. A class of flexure mechanisms with 0?DoS, 1?DoS, 2?DoS and 3?DoS are synthesized respectively based on the Freedom and Constraint Topology method. Their overall compliance matrices in an analytical form formulated within the framework of the screw theory are used to analyze and compare the effect of different number of DoS on the kinetostatic characteristics for flexure mechanisms. The finite element analysis(FEA) simulations are implemented to verify the analytical results. These results show that the higher the DoS is, the smaller the parasitic motion error will be. The flexure model with 3?DoS is optimized according to the overall compliance matrix and then tested by using the FEA simulation. The testing result shows that with the best combination parameters, the parasitic motion error for 3?DoS mechanism is almost eliminated. This research introduces a design principle which can alleviate the unwanted parasitic motion for better accuracy.

Comprehensive kinetostatic modeling and morphology characterization of cable-driven continuum robots for in-situ aero-engine maintenance

In-situ maintenance is of great significance for improving the efficiency and ensuring the safety of aero-engines.The cable-driven continuum robot(CDCR)with twin-pivot compliant mechanisms,which is enabled with flexible deformation capability and confined space accessibility,has emerged as a novel tool that aims to promote the development of intelligence and efficiency for in-situ aero-engine maintenance.The high-fidelity model that describes the kinematic and morphology of CDCR lays the foundation for the accurate operation and control for in-situ maintenance.However,this model was not well addressed in previous literature.In this study,a general kinetostatic modeling and morphology characterization methodology that comprehensively contains the effects of cable-hole friction,gravity,and payloads is proposed for the CDCR with twin-pivot compliant mechanisms.First,a novel cable-hole friction model with the variable friction coefficient and adaptive friction direction criterion is proposed through structure optimization and kinematic parameter analysis.Second,the cable-hole friction,all-component gravities,deflection-induced center-of-gravity shift of compliant joints,and payloads are all considered to deduce a comprehensive kinetostatic model enabled with the capacity of accurate morphology characterization for CDCR.Finally,a compact continuum robot system is integrated to experimentally validate the proposed kinetostatic model and the concept of in-situ aero-engine maintenance.Results indicate that the proposed model precisely predicts the morphology of CDCR and outperforms conventional models.The compact continuum robot system could be considered a novel solution to perform in-situ maintenance tasks of aero-engines in an invasive manner.

Design, modeling, and evaluation of parallel continuum robots: A survey

Parallel continuum robots(PCRs) have attracted increasing attention in the robotics community due to their simplicity in structure,inherence with compliance, and easiness of realization. Over the past decade, a variety of novel designs have been reported to enrich their diversity. However, there is a lack of systematic review of these emerging robots. To this end, this paper conducts a comprehensive survey on the mechanism design, kinetostatic modeling and analysis, and performance evaluation. For these robots, kinetostatic modeling plays a fundamental role throughout the design, analysis, and control stages. A systematic review of the existing approaches for kinetostatic modeling and analysis is provided, and a comparison is made to distinguish their differences. As well, a classification is made according to the characteristics of structure and actuation. In addition, performance evaluation on the workspace, stability, and singularity is also overviewed. Finally, the scenarios of potential applications are elaborated, and future research prospects are discussed. We believe that the information provided in this paper will be particularly useful for those who are interested in PCRs.