This paper focuses on the prediction of the safe autorotation landing operations of a helicopter following engine failure.The autorotation landing procedure is formulated as a nonlinear optimal control problem based o...This paper focuses on the prediction of the safe autorotation landing operations of a helicopter following engine failure.The autorotation landing procedure is formulated as a nonlinear optimal control problem based on an augmented six-degree-of-freedom rigid-body flight dynamic model.First,the cost function and constraints are properly selected.The direct transcription approach is then employed to solve the optimal control problem.For a UH-60 helicopter,the optimal solutions with the rigid-body model are compared with those obtained using a two-dimensional point-mass model.It is found that the optimal solutions using the two different models show reasonably good agreement,and furthermore the optimal solutions using the rigid-body model involve the time histories of angular rates and attitudes,lateral velocity and position,as well as pitch controls.Finally the optimal control formulations with different cost functions are proposed for taking account of 1-s time delay and minimum touchdown speed.The calculated control strategies and trajectories are realistic.展开更多
A hierarchic optimization strategy based on the offline path planning process and online trajectory planning process is presented to solve the trajectory optimization problem of multiple quad-rotor unmanned aerial veh...A hierarchic optimization strategy based on the offline path planning process and online trajectory planning process is presented to solve the trajectory optimization problem of multiple quad-rotor unmanned aerial vehicles in the collaborative assembling task. Firstly, the path planning process is solved by a novel parallel intelligent optimization algorithm, the central force optimization-genetic algorithm （CFO-GA）, which combines the central force optimization （CFO） algorithm with the genetic algorithm （GA）. Because of the immaturity of the CFO, the convergence analysis of the CFO is completed by the stability theory of the linear time-variant discrete-time sys- tems. The results show that the parallel CFO-GA algorithm converges faster than the parallel CFO and the central force optimization-sequential quadratic programming （CFO-SQP） algorithm. Then, the trajectory planning problem is established based on the path planning results. In order to limit the range of the attitude angle and guarantee the fight stability, the optimized object is changed from the ordinary six-degree-of-freedom rigid-body dynamic model to the dynamic model with an inner-loop attitude controller. The results show that the trajectory planning process can be solved by the mature SQP algorithm easily. Finally, the discussion and analysis of the real-time per- formance of the hierarchic optimization strategy are presented around the group number of the wav^oints and the eoual interval time.展开更多
Correct predictions of the behavior of flexible bodies undergoing large rigid-body motions and small elastic vibrations is a subject of major concern in the field of flexible multibody system dynamics. Because of fail...Correct predictions of the behavior of flexible bodies undergoing large rigid-body motions and small elastic vibrations is a subject of major concern in the field of flexible multibody system dynamics. Because of failing to account for the effects of dynamic stiffening, conventional methods based on the linear theories can lead to erroneous results in many practical applications. In this paper, the idea of 'centrifugal potential field', which induced by large overall rotation is introduced, and the motion equation of a coupled rigid-flexible system by employing Hamilton's principle is established. Based on this equation, first it is proved that the elastic motion of the system has periodic property, then by using Frobenius' method its exact solution is obtained. The influences of large overall rigid motion on the elastic vibration mode shape and frequency are analysed through the numerical examples.展开更多
Compliant mechanisms with curved flexure hinges/beams have potential advantages of small spaces,low stress levels,and flexible design parameters,which have attracted considerable attention in precision engineering,met...Compliant mechanisms with curved flexure hinges/beams have potential advantages of small spaces,low stress levels,and flexible design parameters,which have attracted considerable attention in precision engineering,metamaterials,robotics,and so forth.However,serial-parallel configurations with curved flexure hinges/beams often lead to a complicated parametric design.Here,the transfer matrix method is enabled for analysis of both the kinetostatics and dynamics of general serial-parallel compliant mechanisms without deriving laborious formulas or combining other modeling methods.Consequently,serial-parallel compliant mechanisms with curved flexure hinges/beams can be modeled in a straightforward manner based on a single transfer matrix of Timoshenko straight beams using a step-by-step procedure.Theoretical and numerical validations on two customized XY nanopositioners comprised of straight and corrugated flexure units confirm the concise modeling process and high prediction accuracy of the presented approach.In conclusion,the present study provides an enhanced transfer matrix modeling approach to streamline the kinetostatic and dynamic analyses of general serial-parallel compliant mechanisms and beam structures,including curved flexure hinges and irregular-shaped rigid bodies.展开更多
Infinitesimal-rotation finite elements allow creating a linear problem that can be exploited to systematically reduce the number of coordinates and obtain efficient solutions for a wide range of applications,including...Infinitesimal-rotation finite elements allow creating a linear problem that can be exploited to systematically reduce the number of coordinates and obtain efficient solutions for a wide range of applications,including those governed by nonlinear equations.This paper discusses the limitations of conventional infinitesimal-rotation finite elements(FE)in capturing correctly the initial stress-free reference-configuration geometry,and explains the effect of these limitations on the definition of the inertia used in the motion description.An alternative to conventional infinitesimal-rotation finite elements is a new class of elements that allow developing inertia expressions written explicitly in terms of constant coefficients that define accurately the reference-configuration geometry.It is shown that using a geometrically inconsistent(GI)approach that introduces the infinitesimal-rotation coordinates from the outset to replace the interpolation-polynomial coefficients is the main source of the failure to capture correctly the reference-configuration geometry.On the other hand,by using a geometrically consistent(GC)approach that employs the position gradients of the absolute nodal coordinate formulation(ANCF)to define the infinitesimal-rotation coordinates,the reference-configuration geometry can be preserved.Two simple examples of straight and tapered beams are used to demonstrate the basic differences between the two fundamentally different approaches used to introduce the infinitesimal-rotation coordinates.The analysis presented in this study sheds light on the differences between the incremental co-rotational solution procedure,widely used in computational structural mechanics,and the non-incremental floating frame of reference formulation(FFR),widely used in multibody system(MBS)dynamics.展开更多
The influences of nonlinear centrifugal force to large overall attitude motion of coupled rigid-flexible system was investigated. First the nonlinear model of the coupled rigid-flexible system was deduced from the ide...The influences of nonlinear centrifugal force to large overall attitude motion of coupled rigid-flexible system was investigated. First the nonlinear model of the coupled rigid-flexible system was deduced from the idea of “centrifugal potential field', and then the dynamic effects of the nonlinear centrifugal force to system attitude motion were analyzed by approximate calculation; At last, the Lyapunov function based on energy norm was selected, in the condition that only the measured values of attitude and attitude speed are available, and it is proved that the PD feedback control law can ensure the attitude stability during large angle maneuver.展开更多
<strong>Background:</strong><span style="font-family:;" "=""><span style="font-family:Verdana;"> Intraoperative surgical planning tools (ISPTs) used in curren...<strong>Background:</strong><span style="font-family:;" "=""><span style="font-family:Verdana;"> Intraoperative surgical planning tools (ISPTs) used in current-generation robotic arm-assisted total knee arthroplasty (RTKA) systems (such as Navio</span><sup><span style="font-size:12px;font-family:Verdana;"><span lang="ZH-CN" style="font-size:12pt;font-family:宋体;">®</span></span></sup><span style="font-family:Verdana;"> and MAKO</span><sup><span style="font-size:12px;font-family:Verdana;"><span lang="ZH-CN" style="font-size:12pt;font-family:宋体;">®</span></span></sup><span style="font-family:Verdana;">) involve employment of postoperative passive joint balancing. This results in improper ligament tension, which may negatively impact joint stability, which, in turn, may adversely affect patient function after TKA. </span><b><span style="font-family:Verdana;">Methods:</span></b><span style="font-family:Verdana;"> A simulation-enhanced ISPT (SEISPT) that provides insights relating to postoperative active joint mechanics was developed. This involved four steps: 1) validation of a multi-body musculoskeletal model;2) optimization of the validated model;3) use of the validated and optimized model to derive knee performance equations (KPEs), which are equations that relate implant component characteristics to implant component biomechanical responses;and 4) optimization of the KPEs with respect to these responses. In a proof-of-concept study, KPEs that involved two</span></span><span style="font-family:Verdana;"> </span><span style="font-family:Verdana;">com</span><span style="font-family:Verdana;">- </span><span style="font-family:;" "=""><span style="font-family:Verdana;">ponent biomechanical responses that have been shown to strongly correlate with poor proprioception (a common patient complaint post-TKA) were used to calculate optimal positions and orientations of the femoral and tibial components in the TKA design implanted in one subject (as reported in a publicly-available dataset). </span><b><span st展开更多
For the dynamics of a rigid body with a fixed point based on the quaternion and the corresponding generalized momenta, a displacement-based symplectic integration scheme for differential-algebraic equations is propose...For the dynamics of a rigid body with a fixed point based on the quaternion and the corresponding generalized momenta, a displacement-based symplectic integration scheme for differential-algebraic equations is proposed and applied to the Lagrange＇s equations based on dependent generalized momenta. Numerical experiments show that the algorithm possesses such characters as high precision and preserving system invariants. More importantly, the generalized momenta based Lagrange＇s equations show unique advantages over the traditional Lagrange＇s equations in symplectic integrations.展开更多
This paper is the second of two companion papers addressing the dynamics of two coupled masses sliding on analytical surfaces and interacting with one another. The motion occurs under the effect of gravity, the reacti...This paper is the second of two companion papers addressing the dynamics of two coupled masses sliding on analytical surfaces and interacting with one another. The motion occurs under the effect of gravity, the reaction force of the surface and basal friction. The interaction force maintains the masses at a fixed distance and lies on the line connecting them. The equations of motion form a system of ordinary differential equations that are solved through a fourth-order Runge–Kutta numerical scheme. In the first paper we considered an approximate method holding when the line joining the masses is almost tangent to the surface at the instant mass positions. In this second paper we provide a general solution. Firstly, we present special cases in which the system has exact solutions. Second, we consider a series of numerical examples where the interest is focused on the trajectories of the masses and on the intensity and changes of the interaction force.展开更多
Starting from the basic equations of hydrodynamics, the maximum power- type variational principle of the hydrodynamics of viscous fluids was established by Weizang CHIEN in 1984. Through long-term research, it is clar...Starting from the basic equations of hydrodynamics, the maximum power- type variational principle of the hydrodynamics of viscous fluids was established by Weizang CHIEN in 1984. Through long-term research, it is clarified that the maximum power-type variational principle coincides with the Jourdian principle, which is one of the common principles for analytical mechanics. In the paper, the power-type variational principle is extended to rigid-body dynamics, elasto-dynamics, and rigid-elastic：liquid coupling dynamics. The governing equations of the rigid-elastic-liquid coupling dynamics in the liquid-filled system are obtained by deriving the stationary value conditions. The results show that, with the power-type variational principles studied directly in the state space, some transformations in the time domain space may be omitted in the establishing process, and the rigid-elastic-liqUid coupling dynamics can be easily numerically modeled. Moreover, the analysis of the coupling dynamics in the liquid-filled system in this paper agrees well with the numerical analyses of the coupling dynamics in the liquid-filled system offered in the literatures.展开更多
Planar motion of a non-deformable wheel under the action of non-ideal unilateral constraints is considered. The mathematical description of this phenomenon has a form of a non-smooth initial value problem. The non-smo...Planar motion of a non-deformable wheel under the action of non-ideal unilateral constraints is considered. The mathematical description of this phenomenon has a form of a non-smooth initial value problem. The non-smoothness of this problem means that its solution is determined by an absolutely continuous function having a discontinuous first derivative. For this reason, a collision problem describing abrupt changes of velocity has been formulated next to the equations of motion specifying the acceleration. The non-idealness of constraints means that the constraint reaction force includes also a component resulting from the friction between the wheel and the constraints. Differential equations specifying acceleration of the wheel making contact with the constraints and algebraic equations for determining the changes in the wheel’s velocity at the moment of collision have been formulated in the paper. The principal task in these formulations is to determine the reaction forces of the considered constraints. This task is specified by the relationships between acceleration and the constraint reaction force components. In the description of the collision, these relations refer to the post-collision velocities and reaction force impulses. For determining an approximate solution of the formulated wheel motion problem, an original numerical method and a computer program for wheel motion simulation have been developed. Selected results illustrating the changes in displacements and velocity have been presented.展开更多
A configuration point consists of the position and orientation of a rigid body which are fully described by the position of the frame’s origin and the orientation of its axes, relative to the reference frame. We desc...A configuration point consists of the position and orientation of a rigid body which are fully described by the position of the frame’s origin and the orientation of its axes, relative to the reference frame. We describe an algorithm to robustly predict futuristic configurations of a moving target in a time-varying environment. We use the Kalman filter for tracking and motion prediction purposes because it is a very effective and useful estimator. It implements a predictor-corrector type estimator that is optimal in the sense that it minimizes the estimated error covariance. The target motion is unconstrained. The proposed algorithm may be viewed as a seed for a range of applications, one of which is robot motion planning in a time-changing environment. A significant feature of the proposed algorithm (when compared to similar ones) is its ability to embark the prediction process from the first time step;no need to wait for few time steps as in the autoregressive-based systems. Simulation results supports our claims and demonstrate the superiority of the proposed model.展开更多
文摘This paper focuses on the prediction of the safe autorotation landing operations of a helicopter following engine failure.The autorotation landing procedure is formulated as a nonlinear optimal control problem based on an augmented six-degree-of-freedom rigid-body flight dynamic model.First,the cost function and constraints are properly selected.The direct transcription approach is then employed to solve the optimal control problem.For a UH-60 helicopter,the optimal solutions with the rigid-body model are compared with those obtained using a two-dimensional point-mass model.It is found that the optimal solutions using the two different models show reasonably good agreement,and furthermore the optimal solutions using the rigid-body model involve the time histories of angular rates and attitudes,lateral velocity and position,as well as pitch controls.Finally the optimal control formulations with different cost functions are proposed for taking account of 1-s time delay and minimum touchdown speed.The calculated control strategies and trajectories are realistic.
文摘A hierarchic optimization strategy based on the offline path planning process and online trajectory planning process is presented to solve the trajectory optimization problem of multiple quad-rotor unmanned aerial vehicles in the collaborative assembling task. Firstly, the path planning process is solved by a novel parallel intelligent optimization algorithm, the central force optimization-genetic algorithm （CFO-GA）, which combines the central force optimization （CFO） algorithm with the genetic algorithm （GA）. Because of the immaturity of the CFO, the convergence analysis of the CFO is completed by the stability theory of the linear time-variant discrete-time sys- tems. The results show that the parallel CFO-GA algorithm converges faster than the parallel CFO and the central force optimization-sequential quadratic programming （CFO-SQP） algorithm. Then, the trajectory planning problem is established based on the path planning results. In order to limit the range of the attitude angle and guarantee the fight stability, the optimized object is changed from the ordinary six-degree-of-freedom rigid-body dynamic model to the dynamic model with an inner-loop attitude controller. The results show that the trajectory planning process can be solved by the mature SQP algorithm easily. Finally, the discussion and analysis of the real-time per- formance of the hierarchic optimization strategy are presented around the group number of the wav^oints and the eoual interval time.
文摘Correct predictions of the behavior of flexible bodies undergoing large rigid-body motions and small elastic vibrations is a subject of major concern in the field of flexible multibody system dynamics. Because of failing to account for the effects of dynamic stiffening, conventional methods based on the linear theories can lead to erroneous results in many practical applications. In this paper, the idea of 'centrifugal potential field', which induced by large overall rotation is introduced, and the motion equation of a coupled rigid-flexible system by employing Hamilton's principle is established. Based on this equation, first it is proved that the elastic motion of the system has periodic property, then by using Frobenius' method its exact solution is obtained. The influences of large overall rigid motion on the elastic vibration mode shape and frequency are analysed through the numerical examples.
基金funded by the National Natural Science Foundation of China(Grant/Award Numbers:52075179 and 52130508)Jiangsu Policy Guidance Program(International Science and Technology Cooperation)the Belt and Road Initiative Innovative Cooperation Projects:BZ2021016.
文摘Compliant mechanisms with curved flexure hinges/beams have potential advantages of small spaces,low stress levels,and flexible design parameters,which have attracted considerable attention in precision engineering,metamaterials,robotics,and so forth.However,serial-parallel configurations with curved flexure hinges/beams often lead to a complicated parametric design.Here,the transfer matrix method is enabled for analysis of both the kinetostatics and dynamics of general serial-parallel compliant mechanisms without deriving laborious formulas or combining other modeling methods.Consequently,serial-parallel compliant mechanisms with curved flexure hinges/beams can be modeled in a straightforward manner based on a single transfer matrix of Timoshenko straight beams using a step-by-step procedure.Theoretical and numerical validations on two customized XY nanopositioners comprised of straight and corrugated flexure units confirm the concise modeling process and high prediction accuracy of the presented approach.In conclusion,the present study provides an enhanced transfer matrix modeling approach to streamline the kinetostatic and dynamic analyses of general serial-parallel compliant mechanisms and beam structures,including curved flexure hinges and irregular-shaped rigid bodies.
基金supported,in part,by the National Science Foundation(Grant 1852510).
文摘Infinitesimal-rotation finite elements allow creating a linear problem that can be exploited to systematically reduce the number of coordinates and obtain efficient solutions for a wide range of applications,including those governed by nonlinear equations.This paper discusses the limitations of conventional infinitesimal-rotation finite elements(FE)in capturing correctly the initial stress-free reference-configuration geometry,and explains the effect of these limitations on the definition of the inertia used in the motion description.An alternative to conventional infinitesimal-rotation finite elements is a new class of elements that allow developing inertia expressions written explicitly in terms of constant coefficients that define accurately the reference-configuration geometry.It is shown that using a geometrically inconsistent(GI)approach that introduces the infinitesimal-rotation coordinates from the outset to replace the interpolation-polynomial coefficients is the main source of the failure to capture correctly the reference-configuration geometry.On the other hand,by using a geometrically consistent(GC)approach that employs the position gradients of the absolute nodal coordinate formulation(ANCF)to define the infinitesimal-rotation coordinates,the reference-configuration geometry can be preserved.Two simple examples of straight and tapered beams are used to demonstrate the basic differences between the two fundamentally different approaches used to introduce the infinitesimal-rotation coordinates.The analysis presented in this study sheds light on the differences between the incremental co-rotational solution procedure,widely used in computational structural mechanics,and the non-incremental floating frame of reference formulation(FFR),widely used in multibody system(MBS)dynamics.
文摘The influences of nonlinear centrifugal force to large overall attitude motion of coupled rigid-flexible system was investigated. First the nonlinear model of the coupled rigid-flexible system was deduced from the idea of “centrifugal potential field', and then the dynamic effects of the nonlinear centrifugal force to system attitude motion were analyzed by approximate calculation; At last, the Lyapunov function based on energy norm was selected, in the condition that only the measured values of attitude and attitude speed are available, and it is proved that the PD feedback control law can ensure the attitude stability during large angle maneuver.
文摘<strong>Background:</strong><span style="font-family:;" "=""><span style="font-family:Verdana;"> Intraoperative surgical planning tools (ISPTs) used in current-generation robotic arm-assisted total knee arthroplasty (RTKA) systems (such as Navio</span><sup><span style="font-size:12px;font-family:Verdana;"><span lang="ZH-CN" style="font-size:12pt;font-family:宋体;">®</span></span></sup><span style="font-family:Verdana;"> and MAKO</span><sup><span style="font-size:12px;font-family:Verdana;"><span lang="ZH-CN" style="font-size:12pt;font-family:宋体;">®</span></span></sup><span style="font-family:Verdana;">) involve employment of postoperative passive joint balancing. This results in improper ligament tension, which may negatively impact joint stability, which, in turn, may adversely affect patient function after TKA. </span><b><span style="font-family:Verdana;">Methods:</span></b><span style="font-family:Verdana;"> A simulation-enhanced ISPT (SEISPT) that provides insights relating to postoperative active joint mechanics was developed. This involved four steps: 1) validation of a multi-body musculoskeletal model;2) optimization of the validated model;3) use of the validated and optimized model to derive knee performance equations (KPEs), which are equations that relate implant component characteristics to implant component biomechanical responses;and 4) optimization of the KPEs with respect to these responses. In a proof-of-concept study, KPEs that involved two</span></span><span style="font-family:Verdana;"> </span><span style="font-family:Verdana;">com</span><span style="font-family:Verdana;">- </span><span style="font-family:;" "=""><span style="font-family:Verdana;">ponent biomechanical responses that have been shown to strongly correlate with poor proprioception (a common patient complaint post-TKA) were used to calculate optimal positions and orientations of the femoral and tibial components in the TKA design implanted in one subject (as reported in a publicly-available dataset). </span><b><span st
文摘For the dynamics of a rigid body with a fixed point based on the quaternion and the corresponding generalized momenta, a displacement-based symplectic integration scheme for differential-algebraic equations is proposed and applied to the Lagrange＇s equations based on dependent generalized momenta. Numerical experiments show that the algorithm possesses such characters as high precision and preserving system invariants. More importantly, the generalized momenta based Lagrange＇s equations show unique advantages over the traditional Lagrange＇s equations in symplectic integrations.
文摘This paper is the second of two companion papers addressing the dynamics of two coupled masses sliding on analytical surfaces and interacting with one another. The motion occurs under the effect of gravity, the reaction force of the surface and basal friction. The interaction force maintains the masses at a fixed distance and lies on the line connecting them. The equations of motion form a system of ordinary differential equations that are solved through a fourth-order Runge–Kutta numerical scheme. In the first paper we considered an approximate method holding when the line joining the masses is almost tangent to the surface at the instant mass positions. In this second paper we provide a general solution. Firstly, we present special cases in which the system has exact solutions. Second, we consider a series of numerical examples where the interest is focused on the trajectories of the masses and on the intensity and changes of the interaction force.
基金supported by the National Natural Science Foundation of China(No.10272034)the Fundamental Research Funds for the Central Universities of China(No.HEUCF130205)
文摘Starting from the basic equations of hydrodynamics, the maximum power- type variational principle of the hydrodynamics of viscous fluids was established by Weizang CHIEN in 1984. Through long-term research, it is clarified that the maximum power-type variational principle coincides with the Jourdian principle, which is one of the common principles for analytical mechanics. In the paper, the power-type variational principle is extended to rigid-body dynamics, elasto-dynamics, and rigid-elastic：liquid coupling dynamics. The governing equations of the rigid-elastic-liquid coupling dynamics in the liquid-filled system are obtained by deriving the stationary value conditions. The results show that, with the power-type variational principles studied directly in the state space, some transformations in the time domain space may be omitted in the establishing process, and the rigid-elastic-liqUid coupling dynamics can be easily numerically modeled. Moreover, the analysis of the coupling dynamics in the liquid-filled system in this paper agrees well with the numerical analyses of the coupling dynamics in the liquid-filled system offered in the literatures.
文摘Planar motion of a non-deformable wheel under the action of non-ideal unilateral constraints is considered. The mathematical description of this phenomenon has a form of a non-smooth initial value problem. The non-smoothness of this problem means that its solution is determined by an absolutely continuous function having a discontinuous first derivative. For this reason, a collision problem describing abrupt changes of velocity has been formulated next to the equations of motion specifying the acceleration. The non-idealness of constraints means that the constraint reaction force includes also a component resulting from the friction between the wheel and the constraints. Differential equations specifying acceleration of the wheel making contact with the constraints and algebraic equations for determining the changes in the wheel’s velocity at the moment of collision have been formulated in the paper. The principal task in these formulations is to determine the reaction forces of the considered constraints. This task is specified by the relationships between acceleration and the constraint reaction force components. In the description of the collision, these relations refer to the post-collision velocities and reaction force impulses. For determining an approximate solution of the formulated wheel motion problem, an original numerical method and a computer program for wheel motion simulation have been developed. Selected results illustrating the changes in displacements and velocity have been presented.
文摘A configuration point consists of the position and orientation of a rigid body which are fully described by the position of the frame’s origin and the orientation of its axes, relative to the reference frame. We describe an algorithm to robustly predict futuristic configurations of a moving target in a time-varying environment. We use the Kalman filter for tracking and motion prediction purposes because it is a very effective and useful estimator. It implements a predictor-corrector type estimator that is optimal in the sense that it minimizes the estimated error covariance. The target motion is unconstrained. The proposed algorithm may be viewed as a seed for a range of applications, one of which is robot motion planning in a time-changing environment. A significant feature of the proposed algorithm (when compared to similar ones) is its ability to embark the prediction process from the first time step;no need to wait for few time steps as in the autoregressive-based systems. Simulation results supports our claims and demonstrate the superiority of the proposed model.
