In this research,a systematic approach to solving the inverse dynamics of hexarot manipulators is addressed using the methodology of virtual work.For the first time,a closed form of the mathematical formulation of the...In this research,a systematic approach to solving the inverse dynamics of hexarot manipulators is addressed using the methodology of virtual work.For the first time,a closed form of the mathematical formulation of the standard dynamic model is presented for this class of mechanisms.An efficient algorithm for solving this closed-form dynamic model of the mechanism is developed and it is used to simulate the dynamics of the system for different trajectories.Validation of the proposed model is performed using SimMechanics and it is shown that the results of the proposed mathematical model match with the results obtained by the SimMechanics model.展开更多
A systematic methodology for solving the inverse dynamics of the Delta robot is presented.First,the inverse kinematics is solved based on the vector method.A new form of the Jacobi matrix formulized by the vectors is ...A systematic methodology for solving the inverse dynamics of the Delta robot is presented.First,the inverse kinematics is solved based on the vector method.A new form of the Jacobi matrix formulized by the vectors is obtained so the three types kinematics singularities namely inverse, direct and combined types, can be identified with the physical meaning.Then based on the principle of virtual work, a methodology for driving the dynamical equations of motion is developed.Meanwhile the whole actuating torques, the torques caused by the gravity, the velocity and the acceleration are computed respectively in the numerical example. Results show that torque caused by the acceleration term is much bigger than the other two terms.This approach leads to efficient algorithms since the constraint forces and moments of the robot system have been eliminated from the equations of motion and there is no differential equation for the whole procedure when the principle of virtual work is applied to solving the inverse dynamical problem.展开更多
Energy methods and the principle of virtual work are commonly used for obtaining solutions of boundary value problems (BVPs) and initial value problems (IVPs) associated with homogeneous, isotropic and non-homogeneous...Energy methods and the principle of virtual work are commonly used for obtaining solutions of boundary value problems (BVPs) and initial value problems (IVPs) associated with homogeneous, isotropic and non-homogeneous, non-isotropic matter without using (or in the absence of) the mathematical models of the BVPs and the IVPs. These methods are also used for deriving mathematical models for BVPs and IVPs associated with isotropic, homogeneous as well as non-homogeneous, non-isotropic continuous matter. In energy methods when applied to IVPs, one constructs energy functional (<i>I</i>) consisting of kinetic energy, strain energy and the potential energy of loads. The first variation of this energy functional (<em>δI</em>) set to zero is a necessary condition for an extremum of <i>I</i>. In this approach one could use <i>δI</i> = 0 directly in constructing computational processes such as the finite element method or could derive Euler’s equations (differential or partial differential equations) from <i>δI</i> = 0, which is also satisfied by a solution obtained from <i>δI</i> = 0. The Euler’s equations obtained from <i>δI</i> = 0 indeed are the mathematical model associated with the energy functional <i>I</i>. In case of BVPs we follow the same approach except in this case, the energy functional <i>I</i> consists of strain energy and the potential energy of loads. In using the principle of virtual work for BVPs and the IVPs, we can also accomplish the same as described above using energy methods. In this paper we investigate consistency and validity of the mathematical models for isotropic, homogeneous and non-isotropic, non-homogeneous continuous matter for BVPs that are derived using energy functional consisting of strain energy and the potential energy of loads. Similar investigation is also presented for IVPs using energy functional consisting of kinetic energy, strain energy and the potential energy of loads. The computational approaches for BVPs and the IVPs designed using energy functional and principle of virtual work, their consistency and validity are also investigated. Classical continuum mechanics (CCM) principles <i>i.e.</i> conservation and balance laws of CCM with consistent constitutive theories and the elements of calculus of variations are employed in the investigations presented in this paper.展开更多
The virtual displacement principle of elasto-plastic damage mechanics is presented. A linear complementary method for elasto-plastic damage problem is proposed by using FEM technique. This method is applicable to solv...The virtual displacement principle of elasto-plastic damage mechanics is presented. A linear complementary method for elasto-plastic damage problem is proposed by using FEM technique. This method is applicable to solving the damage structure analysis of hardened and softened nonlinear material.展开更多
By expanding the yielding function according toTaylor series and neglecting the high order terms, the elastoplastic constitutive equation is written in a linear complementary form. Based on this linear complementary f...By expanding the yielding function according toTaylor series and neglecting the high order terms, the elastoplastic constitutive equation is written in a linear complementary form. Based on this linear complementary form and the principle of virtual work, a finite element-complementary method is derived for elastoplastic problem. This method is available for materials which satisfy either associated or nonassociated flow rule. In addition, the existence and uniqueness oj solution for the method are also discussed and some useful conclusions are given.展开更多
Soft grippers are favored for handling delicate objects due to their compliance but often have lower load capacities compared to rigid ones.Variable Stiffness Module(VSM)offer a solution,balancing flexibility and load...Soft grippers are favored for handling delicate objects due to their compliance but often have lower load capacities compared to rigid ones.Variable Stiffness Module(VSM)offer a solution,balancing flexibility and load capacity,for which particle jamming is an effective technology for stiffness-tunable robots requiring safe interaction and load capacity.Specific applica-tions,such as rescue scenarios,require quantitative analysis to optimize VSM design parameters,which previous analytical models cannot effectively handle.To address this,a Grey-box model is proposed to analyze the mechanical response of the particle-jamming-based VSM by combining a White-box approach based on the virtual work principle with a Black-box approach that uses a shallow neural network method.The Grey-box model demonstrates a high level of accuracy in predict-ing the VSM force-height mechanical response curves,with errors below 15%in almost 90%of the cases and a maximum error of less than 25%.The model is used to optimize VSM design parameters,particularly those unexplored combinations.Our results from the load capacity and force distribution comparison tests indicate that the VSM,optimized through our methods,quantitatively meets the practical engineering requirements.展开更多
The principle of virtual displacements(PVDs)extended to elasto-thermo-electric problems includes virtual internal elastic,thermal and electric works.The governing equations have displacement vector,temperature and ele...The principle of virtual displacements(PVDs)extended to elasto-thermo-electric problems includes virtual internal elastic,thermal and electric works.The governing equations have displacement vector,temperature and electric potential as primary variables of the problem,and the elasto-thermal,elasto-electric and pure elastic problems are obtained as particular cases by deleting the appropriate contributions in the general elasto-thermo-electric variational statement.The most sensitive issue is given by thermal coupling because the thermo-elastic and thermo-electric effects change depending on the type of load and analysis considered(mechanical load,temperature or electric potential imposed and free vibration analysis).This feature means that the form of the virtual internal thermal work in such variational statements changes depending on the analysis performed and the load applied.Results about multilayered plates and shells suggest the appropriate extension of the variational statement for each analysis,and they give an exhaustive explanation for several forms of the PVD proposed.展开更多
An exoskeleton force feedback dataglove is developed,which uses the pneumatic artificial muscles as actuators.On the basis of the simplified hand model,the motion equation is deduced according to the theory of Denavit...An exoskeleton force feedback dataglove is developed,which uses the pneumatic artificial muscles as actuators.On the basis of the simplified hand model,the motion equation is deduced according to the theory of Denavit-Hartenberg.The model of the equivalent contact forces exerted by the object on the finger is proposed.By the principle of virtual work,the static equilibrium of finger is established.The force Jacobian matrix of finger is calculated,and then the joint torques of the finger when grasping objects are obtained.The theory and structure of the force feedback datagolve are introduced.Based on the theory of motion stabilization of four-bar linkage,the flexion angles of joints are measured.The torques on finger joints caused by the output forces of pneumatic artificial muscles are calculated.The output forces of pneumatic artificial muscle,whose values are controlled by its inner pressure,can be calculated by the joint torques of the finger when grasping objects.The arms of force,driving torques and the needed output forces of pneumatic muscle are calculated for each joint of the index finger.The criterion of output force of pneumatic muscle is given.展开更多
According to the basic idea of dual-complementarity,in a simple and unified way proposed by the author,some basic principles in dynamic theory of elastic materials with voids can be established sys- tematically.In thi...According to the basic idea of dual-complementarity,in a simple and unified way proposed by the author,some basic principles in dynamic theory of elastic materials with voids can be established sys- tematically.In this paper, an important integral relation in terms of convolutions is given,which can be con- sidered as the generalized principle of virtual work in mechanics.Based on this relation,it is possible not on- ly to obtain the principle of virtual work and the reciprocal theorem in dynamic theory of elastic materials with voids,but also to derive systematically the complementary functionals for the eight-field,six-field, four-field and two-field simplified Gurtin-type variational principles.Furthermore,with this approach,the in- trinsic relationship among various principles can be explained clearly.展开更多
For a strip transmission line shielded by rectangular walls, the Green抯 function is helpful to construct the variation expression of the electrostatic energy. Thomson theorem is employed to determine the charge distr...For a strip transmission line shielded by rectangular walls, the Green抯 function is helpful to construct the variation expression of the electrostatic energy. Thomson theorem is employed to determine the charge distribution on the strip. The electrostatic force on each side of the rectangular shield wall is achieved by using the principle of virtual work. The result is easy to be obtained by computerized calculation.展开更多
A geometrical theorem for the static equilibrium of a common-point-force system has been proven by means of virtual-work principle: The equilibrium point of a common-point force system has a minimal weighted distance ...A geometrical theorem for the static equilibrium of a common-point-force system has been proven by means of virtual-work principle: The equilibrium point of a common-point force system has a minimal weighted distance summation to every fixed point arbitrarily given on each force line with a weighing factor proportional to corresponding force value. Especially the mechanical simulating technique for its inverse problem has been realized by means of pulley block. The conclusions for the inverse problem derived from mechanic method are in accordance with that given by the pure mathematical method, and the self-consistence of the theorem and its inverse problem has been demonstrated. Some application examples in engineering, economy and mathematics have been discussed, especially the possible application in the research of molecular structure, has also been predicted.展开更多
文摘In this research,a systematic approach to solving the inverse dynamics of hexarot manipulators is addressed using the methodology of virtual work.For the first time,a closed form of the mathematical formulation of the standard dynamic model is presented for this class of mechanisms.An efficient algorithm for solving this closed-form dynamic model of the mechanism is developed and it is used to simulate the dynamics of the system for different trajectories.Validation of the proposed model is performed using SimMechanics and it is shown that the results of the proposed mathematical model match with the results obtained by the SimMechanics model.
基金Supported by National Natural Science Foundation of China (No. 50375106) andKey Laboratory of Intelligent Manufacturing at Shantou University Grant (No. Imstu-2002-11).
文摘A systematic methodology for solving the inverse dynamics of the Delta robot is presented.First,the inverse kinematics is solved based on the vector method.A new form of the Jacobi matrix formulized by the vectors is obtained so the three types kinematics singularities namely inverse, direct and combined types, can be identified with the physical meaning.Then based on the principle of virtual work, a methodology for driving the dynamical equations of motion is developed.Meanwhile the whole actuating torques, the torques caused by the gravity, the velocity and the acceleration are computed respectively in the numerical example. Results show that torque caused by the acceleration term is much bigger than the other two terms.This approach leads to efficient algorithms since the constraint forces and moments of the robot system have been eliminated from the equations of motion and there is no differential equation for the whole procedure when the principle of virtual work is applied to solving the inverse dynamical problem.
文摘Energy methods and the principle of virtual work are commonly used for obtaining solutions of boundary value problems (BVPs) and initial value problems (IVPs) associated with homogeneous, isotropic and non-homogeneous, non-isotropic matter without using (or in the absence of) the mathematical models of the BVPs and the IVPs. These methods are also used for deriving mathematical models for BVPs and IVPs associated with isotropic, homogeneous as well as non-homogeneous, non-isotropic continuous matter. In energy methods when applied to IVPs, one constructs energy functional (<i>I</i>) consisting of kinetic energy, strain energy and the potential energy of loads. The first variation of this energy functional (<em>δI</em>) set to zero is a necessary condition for an extremum of <i>I</i>. In this approach one could use <i>δI</i> = 0 directly in constructing computational processes such as the finite element method or could derive Euler’s equations (differential or partial differential equations) from <i>δI</i> = 0, which is also satisfied by a solution obtained from <i>δI</i> = 0. The Euler’s equations obtained from <i>δI</i> = 0 indeed are the mathematical model associated with the energy functional <i>I</i>. In case of BVPs we follow the same approach except in this case, the energy functional <i>I</i> consists of strain energy and the potential energy of loads. In using the principle of virtual work for BVPs and the IVPs, we can also accomplish the same as described above using energy methods. In this paper we investigate consistency and validity of the mathematical models for isotropic, homogeneous and non-isotropic, non-homogeneous continuous matter for BVPs that are derived using energy functional consisting of strain energy and the potential energy of loads. Similar investigation is also presented for IVPs using energy functional consisting of kinetic energy, strain energy and the potential energy of loads. The computational approaches for BVPs and the IVPs designed using energy functional and principle of virtual work, their consistency and validity are also investigated. Classical continuum mechanics (CCM) principles <i>i.e.</i> conservation and balance laws of CCM with consistent constitutive theories and the elements of calculus of variations are employed in the investigations presented in this paper.
文摘The virtual displacement principle of elasto-plastic damage mechanics is presented. A linear complementary method for elasto-plastic damage problem is proposed by using FEM technique. This method is applicable to solving the damage structure analysis of hardened and softened nonlinear material.
文摘By expanding the yielding function according toTaylor series and neglecting the high order terms, the elastoplastic constitutive equation is written in a linear complementary form. Based on this linear complementary form and the principle of virtual work, a finite element-complementary method is derived for elastoplastic problem. This method is available for materials which satisfy either associated or nonassociated flow rule. In addition, the existence and uniqueness oj solution for the method are also discussed and some useful conclusions are given.
基金supported by the National Key R&D Program of China(Grant No.2019YFB1311200).
文摘Soft grippers are favored for handling delicate objects due to their compliance but often have lower load capacities compared to rigid ones.Variable Stiffness Module(VSM)offer a solution,balancing flexibility and load capacity,for which particle jamming is an effective technology for stiffness-tunable robots requiring safe interaction and load capacity.Specific applica-tions,such as rescue scenarios,require quantitative analysis to optimize VSM design parameters,which previous analytical models cannot effectively handle.To address this,a Grey-box model is proposed to analyze the mechanical response of the particle-jamming-based VSM by combining a White-box approach based on the virtual work principle with a Black-box approach that uses a shallow neural network method.The Grey-box model demonstrates a high level of accuracy in predict-ing the VSM force-height mechanical response curves,with errors below 15%in almost 90%of the cases and a maximum error of less than 25%.The model is used to optimize VSM design parameters,particularly those unexplored combinations.Our results from the load capacity and force distribution comparison tests indicate that the VSM,optimized through our methods,quantitatively meets the practical engineering requirements.
文摘The principle of virtual displacements(PVDs)extended to elasto-thermo-electric problems includes virtual internal elastic,thermal and electric works.The governing equations have displacement vector,temperature and electric potential as primary variables of the problem,and the elasto-thermal,elasto-electric and pure elastic problems are obtained as particular cases by deleting the appropriate contributions in the general elasto-thermo-electric variational statement.The most sensitive issue is given by thermal coupling because the thermo-elastic and thermo-electric effects change depending on the type of load and analysis considered(mechanical load,temperature or electric potential imposed and free vibration analysis).This feature means that the form of the virtual internal thermal work in such variational statements changes depending on the analysis performed and the load applied.Results about multilayered plates and shells suggest the appropriate extension of the variational statement for each analysis,and they give an exhaustive explanation for several forms of the PVD proposed.
基金This project is supported by National Natural Science Foundation of China(No.50375034).
文摘An exoskeleton force feedback dataglove is developed,which uses the pneumatic artificial muscles as actuators.On the basis of the simplified hand model,the motion equation is deduced according to the theory of Denavit-Hartenberg.The model of the equivalent contact forces exerted by the object on the finger is proposed.By the principle of virtual work,the static equilibrium of finger is established.The force Jacobian matrix of finger is calculated,and then the joint torques of the finger when grasping objects are obtained.The theory and structure of the force feedback datagolve are introduced.Based on the theory of motion stabilization of four-bar linkage,the flexion angles of joints are measured.The torques on finger joints caused by the output forces of pneumatic artificial muscles are calculated.The output forces of pneumatic artificial muscle,whose values are controlled by its inner pressure,can be calculated by the joint torques of the finger when grasping objects.The arms of force,driving torques and the needed output forces of pneumatic muscle are calculated for each joint of the index finger.The criterion of output force of pneumatic muscle is given.
基金The project supported by the Foundation of Zhongshan University Advanced Research Center
文摘According to the basic idea of dual-complementarity,in a simple and unified way proposed by the author,some basic principles in dynamic theory of elastic materials with voids can be established sys- tematically.In this paper, an important integral relation in terms of convolutions is given,which can be con- sidered as the generalized principle of virtual work in mechanics.Based on this relation,it is possible not on- ly to obtain the principle of virtual work and the reciprocal theorem in dynamic theory of elastic materials with voids,but also to derive systematically the complementary functionals for the eight-field,six-field, four-field and two-field simplified Gurtin-type variational principles.Furthermore,with this approach,the in- trinsic relationship among various principles can be explained clearly.
基金Funded by the Key Research Foundation of Sichuan Education Commission(No. 2002A046 )
文摘For a strip transmission line shielded by rectangular walls, the Green抯 function is helpful to construct the variation expression of the electrostatic energy. Thomson theorem is employed to determine the charge distribution on the strip. The electrostatic force on each side of the rectangular shield wall is achieved by using the principle of virtual work. The result is easy to be obtained by computerized calculation.
文摘A geometrical theorem for the static equilibrium of a common-point-force system has been proven by means of virtual-work principle: The equilibrium point of a common-point force system has a minimal weighted distance summation to every fixed point arbitrarily given on each force line with a weighing factor proportional to corresponding force value. Especially the mechanical simulating technique for its inverse problem has been realized by means of pulley block. The conclusions for the inverse problem derived from mechanic method are in accordance with that given by the pure mathematical method, and the self-consistence of the theorem and its inverse problem has been demonstrated. Some application examples in engineering, economy and mathematics have been discussed, especially the possible application in the research of molecular structure, has also been predicted.
