Laboratory experiments were conducted for falling U-chain,but explicit analytic form of the general equations of motion was not presented.Several modeling methods were developed for fish robots,however they just focus...Laboratory experiments were conducted for falling U-chain,but explicit analytic form of the general equations of motion was not presented.Several modeling methods were developed for fish robots,however they just focused on the whole fish’s locomotion which does little favor to understand the detailed swimming behavior of fish.Udwadia-Kalaba theory is used to model these two multi-body systems and obtain explicit analytic equations of motion.For falling U-chain,the mass matrix is non-singular.Second-order constraints are used to get the constraint force and equations of motion and the numerical simulation is conducted.Simulation results show that the chain tip falls faster than the freely falling body.For fish robot,two-joint Carangiform fish robot is focused on.Quasi-steady wing theory is used to approximately calculate fluid lift force acting on the caudal fin.Based on the obtained explicit analytic equations of motion(the mass matrix is singular),propulsive characteristics of each part of the fish robot are obtained.Through these two cases of U chain and fish robot,how to use Udwadia-Kalaba equation to obtain the dynamical model is shown and the modeling methodology for multi-body systems is presented.It is also shown that Udwadia-Kalaba theory is applicable to systems whether or not their mass matrices are singular.In the whole process of applying Udwadia-Kalaba equation,Lagrangian multipliers and quasi-coordinates are not used.Udwadia-Kalaba theory is creatively applied to dynamical modeling of falling U-chain and fish robot problems and explicit analytic equations of motion are obtained.展开更多
The objective of this investigation is to examine the correctness and efficiency of the choice of boundary conditions when using assumed mode approach to simulate flexible multi-body systems. The displacement field du...The objective of this investigation is to examine the correctness and efficiency of the choice of boundary conditions when using assumed mode approach to simulate flexible multi-body systems. The displacement field due to deformation is approximated by the Rayleigh-Ritz assumed modes in floating frame of reference （FFR） formulation. The deformations obtained by the absolute nodal coordinate （ANC） formulation which are transformed by two sets of reference coordinates are introduced as a criterion to verify the accuracy of the simulation results by using the FFR formulation. The relationship between the deformations obtained from different boundary conditions is revealed. Nu- merical simulation examples demonstrate that the assumed modes with cantilevered-free, simply-supported and free- free boundary conditions without inclusion of rigid body modes are suitable for simulation of flexible multi-body system with large over all motion, and the same physical deformation can be obtained using those mode functions, differ only by a coordinate transformation. It is also shown that when using mode shapes with statically indeterminate boundary conditions, significant error may occur. Furthermore, the slider crank mechanism with rigid crank is accurate enough for investigating boundary condition problem of flexible multi-body system, which cost significant less simulating time.展开更多
One of the important trends in precision machining is the development ofreal-time error compensation technique. The error compensation for multi-axis CNC machine tools isvery difficult and attractive. The modeling for...One of the important trends in precision machining is the development ofreal-time error compensation technique. The error compensation for multi-axis CNC machine tools isvery difficult and attractive. The modeling for the geometric error of five-axis CNC machine toolsbased on multi-body systems is proposed. And the key technique of the compensation―identifyinggeometric error parameters―is developed. The simulation of cutting workpiece to verify the modelingbased on the multi-body systems is also considered.展开更多
This paper concentrates on the aeroelasticity analysis of rotor blade and rotor control systems. A new multi-body dynamics model is established to predict both rotor pitch link loads and swashplate servo loads. Two he...This paper concentrates on the aeroelasticity analysis of rotor blade and rotor control systems. A new multi-body dynamics model is established to predict both rotor pitch link loads and swashplate servo loads. Two helicopter rotors of UH-60A and SA349/2, both operating in two critical flight conditions, high-speed flight and high-thrust flight, are studied. The analysis shows good agreements with the flight test data and the calculation results using CAMRAD II. The mechanisms of rotor control loads are then analyzed in details based on the present predictions and the flight test data. In high-speed conditions, the pitch link loads are dominated by the integral of blade pitching moments, which are generated by cyclic pitch control. In high-thrust conditions, the positive pitching loads in the advancing side are caused by high collective pitch angle, and dynamic stall in the retreating side excites high-frequency responses. The swashplate servo loads are predominated by the rotor pitch link loads, and the inertia of the swashplate has significant effects on high-frequency harmonics of the servo loads.展开更多
Incorporating quasi-periodic orbits into the preliminary design process offers a wide range of options to meet mission constraints and address the challenges in a complex trade space.In this investigation,linear stabi...Incorporating quasi-periodic orbits into the preliminary design process offers a wide range of options to meet mission constraints and address the challenges in a complex trade space.In this investigation,linear stability and quasi-periodic orbit family continuation schemes are examined to meet various types of constraints.Applications in eclipse avoidance and transfer design are examined by leveraging quasi-periodic orbits and their associated hyperbolic manifolds in the lunar region.Solutions are transitioned to an ephemeris model to validate that geometries are maintained in higher-fidelity models.When the natural dynamical structures associated with quasi-periodic orbits are leveraged,novel trajectory solutions can emerge.展开更多
文摘Laboratory experiments were conducted for falling U-chain,but explicit analytic form of the general equations of motion was not presented.Several modeling methods were developed for fish robots,however they just focused on the whole fish’s locomotion which does little favor to understand the detailed swimming behavior of fish.Udwadia-Kalaba theory is used to model these two multi-body systems and obtain explicit analytic equations of motion.For falling U-chain,the mass matrix is non-singular.Second-order constraints are used to get the constraint force and equations of motion and the numerical simulation is conducted.Simulation results show that the chain tip falls faster than the freely falling body.For fish robot,two-joint Carangiform fish robot is focused on.Quasi-steady wing theory is used to approximately calculate fluid lift force acting on the caudal fin.Based on the obtained explicit analytic equations of motion(the mass matrix is singular),propulsive characteristics of each part of the fish robot are obtained.Through these two cases of U chain and fish robot,how to use Udwadia-Kalaba equation to obtain the dynamical model is shown and the modeling methodology for multi-body systems is presented.It is also shown that Udwadia-Kalaba theory is applicable to systems whether or not their mass matrices are singular.In the whole process of applying Udwadia-Kalaba equation,Lagrangian multipliers and quasi-coordinates are not used.Udwadia-Kalaba theory is creatively applied to dynamical modeling of falling U-chain and fish robot problems and explicit analytic equations of motion are obtained.
基金supported by the National Natural Science Foundation of China (10872126)the Research Fund of the Doctoral Program of Higher Education of China (20100073110007)
文摘The objective of this investigation is to examine the correctness and efficiency of the choice of boundary conditions when using assumed mode approach to simulate flexible multi-body systems. The displacement field due to deformation is approximated by the Rayleigh-Ritz assumed modes in floating frame of reference （FFR） formulation. The deformations obtained by the absolute nodal coordinate （ANC） formulation which are transformed by two sets of reference coordinates are introduced as a criterion to verify the accuracy of the simulation results by using the FFR formulation. The relationship between the deformations obtained from different boundary conditions is revealed. Nu- merical simulation examples demonstrate that the assumed modes with cantilevered-free, simply-supported and free- free boundary conditions without inclusion of rigid body modes are suitable for simulation of flexible multi-body system with large over all motion, and the same physical deformation can be obtained using those mode functions, differ only by a coordinate transformation. It is also shown that when using mode shapes with statically indeterminate boundary conditions, significant error may occur. Furthermore, the slider crank mechanism with rigid crank is accurate enough for investigating boundary condition problem of flexible multi-body system, which cost significant less simulating time.
基金This project is supported by National Natural Science Foundation of China (No.E059905019)
文摘One of the important trends in precision machining is the development ofreal-time error compensation technique. The error compensation for multi-axis CNC machine tools isvery difficult and attractive. The modeling for the geometric error of five-axis CNC machine toolsbased on multi-body systems is proposed. And the key technique of the compensation―identifyinggeometric error parameters―is developed. The simulation of cutting workpiece to verify the modelingbased on the multi-body systems is also considered.
文摘This paper concentrates on the aeroelasticity analysis of rotor blade and rotor control systems. A new multi-body dynamics model is established to predict both rotor pitch link loads and swashplate servo loads. Two helicopter rotors of UH-60A and SA349/2, both operating in two critical flight conditions, high-speed flight and high-thrust flight, are studied. The analysis shows good agreements with the flight test data and the calculation results using CAMRAD II. The mechanisms of rotor control loads are then analyzed in details based on the present predictions and the flight test data. In high-speed conditions, the pitch link loads are dominated by the integral of blade pitching moments, which are generated by cyclic pitch control. In high-thrust conditions, the positive pitching loads in the advancing side are caused by high collective pitch angle, and dynamic stall in the retreating side excites high-frequency responses. The swashplate servo loads are predominated by the rotor pitch link loads, and the inertia of the swashplate has significant effects on high-frequency harmonics of the servo loads.
文摘Incorporating quasi-periodic orbits into the preliminary design process offers a wide range of options to meet mission constraints and address the challenges in a complex trade space.In this investigation,linear stability and quasi-periodic orbit family continuation schemes are examined to meet various types of constraints.Applications in eclipse avoidance and transfer design are examined by leveraging quasi-periodic orbits and their associated hyperbolic manifolds in the lunar region.Solutions are transitioned to an ephemeris model to validate that geometries are maintained in higher-fidelity models.When the natural dynamical structures associated with quasi-periodic orbits are leveraged,novel trajectory solutions can emerge.
