Mohammad Vakil - Academia.edu (original) (raw)
Papers by Mohammad Vakil
errors of assumed shape modeling for flexible-link manipulators
The assumed mode shape method has been widely used to derive finite degree-of-freedom dynamic mod... more The assumed mode shape method has been widely used to derive finite degree-of-freedom dynamic models for flexible-link manipulators, which theoretically have infinite degree-of-freedom dynamics. For a single flexible manipulator, this approximation changes locations of the zeros of transfer functions between base torque and end-effector displacement. The change in locations of zeros considerably affects accuracy of the model and therefore the performance of model-based controllers. This article presents a comprehensive study on the change in locations of zeros due to the truncation associated with assumed mode shape method. It is shown that the locations of approximate zeros depend on four non-dimensional parameters, whereas the locations of analytical zeros depend on only two non-dimensional parameters. Approximate zeros are obtained from assumed mode shape method models, whereas analytical zeros are derived from infinite order models. A thorough study of the differences between ap...
Transactions of the Canadian Society for Mechanical Engineering, 2009
International Journal of Non-Linear Mechanics, 2009
ABSTRACT In this paper a new controller for the end-effector trajectory tracking (EETT) of multil... more ABSTRACT In this paper a new controller for the end-effector trajectory tracking (EETT) of multilink flexible manipulators (MLFM) is introduced. The new controller is derived utilizing the concept of the integral manifold of the singularly perturbed differential equations.Based on the new controller, to reduce the end-effector trajectory tracking error, a corrective term of order ε2 has to be added to the computed torque command (CTC) of the rigid link counterpart of the MLFM, where the parameter ε=1/2πf and f is the smallest non-zero natural frequency (first natural frequency) of the MLFM in the specified range of operation of the manipulator. The implementation of the new controller does not require measurement of the time derivative of the links’ lateral deflections, which may be practically impossible. This is achieved since the time derivative of the links’ lateral deflections is estimated by using an observer, which is designed based on the gain-scheduling technique. The stability of the proposed controller is proven using the Lyapunov criterion. Simulation results showed the effectiveness of the new controller.One of the main contributions of this work is in the derivation of a new EETT controller for the MLFM, based on the integral manifold concept, which: (1) requires the fewest corrective terms in addition to the CTC and (2) its calculation effort is minimized.
Journal of Vibration and Acoustics, 2011
In this article, by combining the assumed mode shape method and the Lagrange’s equations, a new a... more In this article, by combining the assumed mode shape method and the Lagrange’s equations, a new and efficient method is introduced to obtain a closed-form finite dimensional dynamic model for planar Flexible-link Flexible-joint Manipulators (FFs). To derive the dynamic model, this new method separates (disassembles) a FF into two subsystems. The first subsystem is the counterpart of the FF but without joints’ flexibilities and rotors’ mass moment of inertias; this subsystem is referred to as a Flexible-link Rigid-joint manipulator (FR). The second subsystem has the joints’ flexibilities and rotors’ mass moment of inertias, which are excluded from the FR; this subsystem is called Flexible-Inertia entities (FI). While the method proposed here employs the Lagrange’s equations, it neither requires the derivation of the lengthy Lagrangian function nor its complex derivative calculations. This new method only requires the Lagrangain function evaluation and its derivative calculations for ...
Scientia Iranica
In this paper, a novel spatial six-degree-of freedom parallel manipulator actuated by three base-... more In this paper, a novel spatial six-degree-of freedom parallel manipulator actuated by three base-mounted partial spherical actuators is studied. This new parallel manipulator consists of a base platform and a moving platform, which are connected by three legs. Each leg of the manipulator is composed of a spherical joint, prismatic joint and universal joint. The base-mounted partial spherical actuators can only specify the direction of their corresponding legs. In other words, the spin of each leg is a passive degree-of-freedom. The inverse pose and forward pose of the new mechanism are described. In the inverse pose kinematics, active joint variables are calculated with no need for evaluation of the passive joint variables. To solve the forward pose problem, a much simpler method compared to the traditional method is introduced. Closed form relations for the inverse and forward rate kinematics are proposed. Finally, two sets of singular connguration of the newly introduced manipulat...
Volume 7: 29th Mechanisms and Robotics Conference, Parts A and B, 2005
ABSTRACT In this article kinematic analysis of a 3 Leg-Spherically Actuated (3SA) parallel manipu... more ABSTRACT In this article kinematic analysis of a 3 Leg-Spherically Actuated (3SA) parallel manipulator will be addressed. Since each leg has a spherical actuator (three inputs for each leg) and manipulator has three legs; totally, there are nine inputs. Due to the fact that the manipulator has six degree of freedom, only six independent inputs are needed. Thus actuation could be done in different ways. If the triangles representing base and platform are equilateral, there are twenty different ways of actuation that should be studied during forward kinematic analysis. Rather than adopting the standard Denavit-Hartenberg approach, a simple method for forward kinematic analysis for all these different ways of twenty ways has been introduced. Considering all these ways, it will be shown that at least two and at most six nonlinear algebraic equations should be solved during forward kinematic analysis, while choosing the standard approach twelve nonlinear equations should be solved for each way of actuation. A unique inverse kinematic method has been presented. The singularly analysis for all these different ways of actuation has also been studied. For two out of the twenty different ways, closed form solutions for the singularity analysis have been obtained, for other ways; conditions which result in singularity configuration has been presented and simulation justified the proposed criteria.
Volume 2: 28th Biennial Mechanisms and Robotics Conference, Parts A and B, 2004
In this paper, a novel six degrees-of-freedom (6-DOF) parallel manipulator actuated by three base... more In this paper, a novel six degrees-of-freedom (6-DOF) parallel manipulator actuated by three base-mounted partial spherical actuators is proposed. The parallel manipulator consists of a base, a moving platform and three connecting legs. Each leg has spherical (S), prismatic (P) and universal (U) joints (SPU) in serial manner. The spherical joints are partially actuated due to the fact that the actuators of each leg are used only to specify its leg’s direction. The inverse and forward pose kinematics as well as the singularity points of the aforementioned mechanism is described in the article. In the inverse pose kinematics, active joint variables could be calculated with no need for the evaluation of passive joint variables. It will be shown that the inverse pose kinematics has sixty-four (64) solutions (64 different configurations exists for the inverse pose problem). In the forward pose kinematics, instead of twelve nonlinear equations derived by equaling the transformation matric...
Proceedings 2007 IEEE International Conference on Robotics and Automation, 2007
IEEE Conference on Robotics, Automation and Mechatronics, 2004.
... Hassan Zohoor Profeesor Mechanical Engineering Department Sharif University of Technology Teh... more ... Hassan Zohoor Profeesor Mechanical Engineering Department Sharif University of Technology Tehran, 11365-9567, Iran zohoor@sharif.edu Vakit_ mohammad@yahoo. com ... into dynamical formulation. To omit the Lagrange mUltipliers ...
Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science, 2012
The assumed mode shape method has been widely used to derive finite degree-of-freedom dynamic mod... more The assumed mode shape method has been widely used to derive finite degree-of-freedom dynamic models for flexible-link manipulators, which theoretically have infinite degree-of-freedom dynamics. For a single flexible manipulator, this approximation changes locations of the zeros of transfer functions between base torque and end-effector displacement. The change in locations of zeros considerably affects accuracy of the model and therefore the performance of model-based controllers. This article presents a comprehensive study on the change in locations of zeros due to the truncation associated with assumed mode shape method. It is shown that the locations of approximate zeros depend on four non-dimensional parameters, whereas the locations of analytical zeros depend on only two non-dimensional parameters. Approximate zeros are obtained from assumed mode shape method models, whereas analytical zeros are derived from infinite order models. A thorough study of the differences between ap...
Mechanism and Machine Theory, 2008
Mechanism and Machine Theory, 2006
International Journal of Systems Science, 2011
ABSTRACT A new controller for the end-effector trajectory tracking of a single flexible link mani... more ABSTRACT A new controller for the end-effector trajectory tracking of a single flexible link manipulator is introduced. The linear dynamic model of the single flexible link manipulator is expressed in the singularly perturbed form. To reduce the end-effector trajectory tracking error, a corrective torque is added to the computed torque command of the rigid link counterpart of the single flexible link manipulator. The corrective torque is derived based on the concept of the integral manifold of the singularly perturbed differential equations. This corrective torque is of order ε where , and f is the fundamental natural frequency of the single flexible link manipulator. The implementation of the introduced technique does not require the full-state measurements since by designing an observer, the time derivative of the link's lateral deflection is estimated. The stability proof of the new controller, which is based on the Lyapunov criterion, is presented. The results of the simulation and experimental studies are also included to, respectively, show the effectiveness and feasibility of the new controller.
Transactions of the Canadian Society for Mechanical Engineering, 2009
A new causal dynamic end-effector inversion method for a single flexible link manipulator is intr... more A new causal dynamic end-effector inversion method for a single flexible link manipulator is introduced. Contrary to the available non-causal inversion technique, this method does not lead to pre-actuation and works even in the presence of the purely imaginary zeros for the transfer function. Based on this approach, the desired end-effector trajectory is divided into a finite number of segments. In each segment, the desired trajectory is redefined so that a bounded continuous torque through causal dynamic inversion is obtained. The redefinition of the desired trajectory at each segment employs summation of stable exponential functions. This leads to a family of answers for the redefined trajectory, which is an advantage for control engineers. The results of the simulation and experimental studies show the feasibility and effectiveness of this new technique.
In this article, a study of the zeros of the transfer function, between the base torque and the e... more In this article, a study of the zeros of the transfer function, between the base torque and the end-effector displacement, for flexible link manipulators is performed. The analysis is carried out on a single flexible link manipulator with the initial part of the link being rigid. This type of manipulator is referred to as a slewing single rigid—flexible link manipulator (SRFLM). A new method for finding the zeros of the transfer function of an SRFLM without using the corresponding transfer function is introduced. The changes of the locations of the zeros of an SRFLM owing to the changes in all the physical parameters (PPs) are investigated. It is shown that there are PPs where the increase in their values moves the zeros further from the imaginary axis; while by increasing the values of some other PPs the zeros become closer to the imaginary axis. Finally, there are PPs where the locations of the zeros are independent of their values. These findings will be beneficial in the design as well as control of flexible link manipulators and are among the main contributions of this work.
Volume 2: 28th Biennial Mechanisms and Robotics Conference, Parts A and B, 2004
ABSTRACT In this paper, a novel six degrees-of-freedom (6-DOF) parallel manipulator actuated by t... more ABSTRACT In this paper, a novel six degrees-of-freedom (6-DOF) parallel manipulator actuated by three base-mounted partial spherical actuators is proposed. The parallel manipulator consists of a base, a moving platform and three connecting legs. Each leg has spherical (S), prismatic (P) and universal (U) joints (SPU) in serial manner. The spherical joints are partially actuated due to the fact that the actuators of each leg are used only to specify its leg’s direction. The inverse and forward pose kinematics as well as the singularity points of the aforementioned mechanism is described in the article. In the inverse pose kinematics, active joint variables could be calculated with no need for the evaluation of passive joint variables. It will be shown that the inverse pose kinematics has sixty-four (64) solutions (64 different configurations exists for the inverse pose problem). In the forward pose kinematics, instead of twelve nonlinear equations derived by equaling the transformation matrices of each leg through Denavit-Hartenberg notation, only three nonlinear equations with less nonlinearity could be solved via numerical method, and therefore the numerical method converges more rapidly to the answer. Finally two different sets of singularity points with different natures are obtained.
Volume 2: 32nd Mechanisms and Robotics Conference, Parts A and B, 2008
errors of assumed shape modeling for flexible-link manipulators
The assumed mode shape method has been widely used to derive finite degree-of-freedom dynamic mod... more The assumed mode shape method has been widely used to derive finite degree-of-freedom dynamic models for flexible-link manipulators, which theoretically have infinite degree-of-freedom dynamics. For a single flexible manipulator, this approximation changes locations of the zeros of transfer functions between base torque and end-effector displacement. The change in locations of zeros considerably affects accuracy of the model and therefore the performance of model-based controllers. This article presents a comprehensive study on the change in locations of zeros due to the truncation associated with assumed mode shape method. It is shown that the locations of approximate zeros depend on four non-dimensional parameters, whereas the locations of analytical zeros depend on only two non-dimensional parameters. Approximate zeros are obtained from assumed mode shape method models, whereas analytical zeros are derived from infinite order models. A thorough study of the differences between ap...
Transactions of the Canadian Society for Mechanical Engineering, 2009
International Journal of Non-Linear Mechanics, 2009
ABSTRACT In this paper a new controller for the end-effector trajectory tracking (EETT) of multil... more ABSTRACT In this paper a new controller for the end-effector trajectory tracking (EETT) of multilink flexible manipulators (MLFM) is introduced. The new controller is derived utilizing the concept of the integral manifold of the singularly perturbed differential equations.Based on the new controller, to reduce the end-effector trajectory tracking error, a corrective term of order ε2 has to be added to the computed torque command (CTC) of the rigid link counterpart of the MLFM, where the parameter ε=1/2πf and f is the smallest non-zero natural frequency (first natural frequency) of the MLFM in the specified range of operation of the manipulator. The implementation of the new controller does not require measurement of the time derivative of the links’ lateral deflections, which may be practically impossible. This is achieved since the time derivative of the links’ lateral deflections is estimated by using an observer, which is designed based on the gain-scheduling technique. The stability of the proposed controller is proven using the Lyapunov criterion. Simulation results showed the effectiveness of the new controller.One of the main contributions of this work is in the derivation of a new EETT controller for the MLFM, based on the integral manifold concept, which: (1) requires the fewest corrective terms in addition to the CTC and (2) its calculation effort is minimized.
Journal of Vibration and Acoustics, 2011
In this article, by combining the assumed mode shape method and the Lagrange’s equations, a new a... more In this article, by combining the assumed mode shape method and the Lagrange’s equations, a new and efficient method is introduced to obtain a closed-form finite dimensional dynamic model for planar Flexible-link Flexible-joint Manipulators (FFs). To derive the dynamic model, this new method separates (disassembles) a FF into two subsystems. The first subsystem is the counterpart of the FF but without joints’ flexibilities and rotors’ mass moment of inertias; this subsystem is referred to as a Flexible-link Rigid-joint manipulator (FR). The second subsystem has the joints’ flexibilities and rotors’ mass moment of inertias, which are excluded from the FR; this subsystem is called Flexible-Inertia entities (FI). While the method proposed here employs the Lagrange’s equations, it neither requires the derivation of the lengthy Lagrangian function nor its complex derivative calculations. This new method only requires the Lagrangain function evaluation and its derivative calculations for ...
Scientia Iranica
In this paper, a novel spatial six-degree-of freedom parallel manipulator actuated by three base-... more In this paper, a novel spatial six-degree-of freedom parallel manipulator actuated by three base-mounted partial spherical actuators is studied. This new parallel manipulator consists of a base platform and a moving platform, which are connected by three legs. Each leg of the manipulator is composed of a spherical joint, prismatic joint and universal joint. The base-mounted partial spherical actuators can only specify the direction of their corresponding legs. In other words, the spin of each leg is a passive degree-of-freedom. The inverse pose and forward pose of the new mechanism are described. In the inverse pose kinematics, active joint variables are calculated with no need for evaluation of the passive joint variables. To solve the forward pose problem, a much simpler method compared to the traditional method is introduced. Closed form relations for the inverse and forward rate kinematics are proposed. Finally, two sets of singular connguration of the newly introduced manipulat...
Volume 7: 29th Mechanisms and Robotics Conference, Parts A and B, 2005
ABSTRACT In this article kinematic analysis of a 3 Leg-Spherically Actuated (3SA) parallel manipu... more ABSTRACT In this article kinematic analysis of a 3 Leg-Spherically Actuated (3SA) parallel manipulator will be addressed. Since each leg has a spherical actuator (three inputs for each leg) and manipulator has three legs; totally, there are nine inputs. Due to the fact that the manipulator has six degree of freedom, only six independent inputs are needed. Thus actuation could be done in different ways. If the triangles representing base and platform are equilateral, there are twenty different ways of actuation that should be studied during forward kinematic analysis. Rather than adopting the standard Denavit-Hartenberg approach, a simple method for forward kinematic analysis for all these different ways of twenty ways has been introduced. Considering all these ways, it will be shown that at least two and at most six nonlinear algebraic equations should be solved during forward kinematic analysis, while choosing the standard approach twelve nonlinear equations should be solved for each way of actuation. A unique inverse kinematic method has been presented. The singularly analysis for all these different ways of actuation has also been studied. For two out of the twenty different ways, closed form solutions for the singularity analysis have been obtained, for other ways; conditions which result in singularity configuration has been presented and simulation justified the proposed criteria.
Volume 2: 28th Biennial Mechanisms and Robotics Conference, Parts A and B, 2004
In this paper, a novel six degrees-of-freedom (6-DOF) parallel manipulator actuated by three base... more In this paper, a novel six degrees-of-freedom (6-DOF) parallel manipulator actuated by three base-mounted partial spherical actuators is proposed. The parallel manipulator consists of a base, a moving platform and three connecting legs. Each leg has spherical (S), prismatic (P) and universal (U) joints (SPU) in serial manner. The spherical joints are partially actuated due to the fact that the actuators of each leg are used only to specify its leg’s direction. The inverse and forward pose kinematics as well as the singularity points of the aforementioned mechanism is described in the article. In the inverse pose kinematics, active joint variables could be calculated with no need for the evaluation of passive joint variables. It will be shown that the inverse pose kinematics has sixty-four (64) solutions (64 different configurations exists for the inverse pose problem). In the forward pose kinematics, instead of twelve nonlinear equations derived by equaling the transformation matric...
Proceedings 2007 IEEE International Conference on Robotics and Automation, 2007
IEEE Conference on Robotics, Automation and Mechatronics, 2004.
... Hassan Zohoor Profeesor Mechanical Engineering Department Sharif University of Technology Teh... more ... Hassan Zohoor Profeesor Mechanical Engineering Department Sharif University of Technology Tehran, 11365-9567, Iran zohoor@sharif.edu Vakit_ mohammad@yahoo. com ... into dynamical formulation. To omit the Lagrange mUltipliers ...
Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science, 2012
The assumed mode shape method has been widely used to derive finite degree-of-freedom dynamic mod... more The assumed mode shape method has been widely used to derive finite degree-of-freedom dynamic models for flexible-link manipulators, which theoretically have infinite degree-of-freedom dynamics. For a single flexible manipulator, this approximation changes locations of the zeros of transfer functions between base torque and end-effector displacement. The change in locations of zeros considerably affects accuracy of the model and therefore the performance of model-based controllers. This article presents a comprehensive study on the change in locations of zeros due to the truncation associated with assumed mode shape method. It is shown that the locations of approximate zeros depend on four non-dimensional parameters, whereas the locations of analytical zeros depend on only two non-dimensional parameters. Approximate zeros are obtained from assumed mode shape method models, whereas analytical zeros are derived from infinite order models. A thorough study of the differences between ap...
Mechanism and Machine Theory, 2008
Mechanism and Machine Theory, 2006
International Journal of Systems Science, 2011
ABSTRACT A new controller for the end-effector trajectory tracking of a single flexible link mani... more ABSTRACT A new controller for the end-effector trajectory tracking of a single flexible link manipulator is introduced. The linear dynamic model of the single flexible link manipulator is expressed in the singularly perturbed form. To reduce the end-effector trajectory tracking error, a corrective torque is added to the computed torque command of the rigid link counterpart of the single flexible link manipulator. The corrective torque is derived based on the concept of the integral manifold of the singularly perturbed differential equations. This corrective torque is of order ε where , and f is the fundamental natural frequency of the single flexible link manipulator. The implementation of the introduced technique does not require the full-state measurements since by designing an observer, the time derivative of the link's lateral deflection is estimated. The stability proof of the new controller, which is based on the Lyapunov criterion, is presented. The results of the simulation and experimental studies are also included to, respectively, show the effectiveness and feasibility of the new controller.
Transactions of the Canadian Society for Mechanical Engineering, 2009
A new causal dynamic end-effector inversion method for a single flexible link manipulator is intr... more A new causal dynamic end-effector inversion method for a single flexible link manipulator is introduced. Contrary to the available non-causal inversion technique, this method does not lead to pre-actuation and works even in the presence of the purely imaginary zeros for the transfer function. Based on this approach, the desired end-effector trajectory is divided into a finite number of segments. In each segment, the desired trajectory is redefined so that a bounded continuous torque through causal dynamic inversion is obtained. The redefinition of the desired trajectory at each segment employs summation of stable exponential functions. This leads to a family of answers for the redefined trajectory, which is an advantage for control engineers. The results of the simulation and experimental studies show the feasibility and effectiveness of this new technique.
In this article, a study of the zeros of the transfer function, between the base torque and the e... more In this article, a study of the zeros of the transfer function, between the base torque and the end-effector displacement, for flexible link manipulators is performed. The analysis is carried out on a single flexible link manipulator with the initial part of the link being rigid. This type of manipulator is referred to as a slewing single rigid—flexible link manipulator (SRFLM). A new method for finding the zeros of the transfer function of an SRFLM without using the corresponding transfer function is introduced. The changes of the locations of the zeros of an SRFLM owing to the changes in all the physical parameters (PPs) are investigated. It is shown that there are PPs where the increase in their values moves the zeros further from the imaginary axis; while by increasing the values of some other PPs the zeros become closer to the imaginary axis. Finally, there are PPs where the locations of the zeros are independent of their values. These findings will be beneficial in the design as well as control of flexible link manipulators and are among the main contributions of this work.
Volume 2: 28th Biennial Mechanisms and Robotics Conference, Parts A and B, 2004
ABSTRACT In this paper, a novel six degrees-of-freedom (6-DOF) parallel manipulator actuated by t... more ABSTRACT In this paper, a novel six degrees-of-freedom (6-DOF) parallel manipulator actuated by three base-mounted partial spherical actuators is proposed. The parallel manipulator consists of a base, a moving platform and three connecting legs. Each leg has spherical (S), prismatic (P) and universal (U) joints (SPU) in serial manner. The spherical joints are partially actuated due to the fact that the actuators of each leg are used only to specify its leg’s direction. The inverse and forward pose kinematics as well as the singularity points of the aforementioned mechanism is described in the article. In the inverse pose kinematics, active joint variables could be calculated with no need for the evaluation of passive joint variables. It will be shown that the inverse pose kinematics has sixty-four (64) solutions (64 different configurations exists for the inverse pose problem). In the forward pose kinematics, instead of twelve nonlinear equations derived by equaling the transformation matrices of each leg through Denavit-Hartenberg notation, only three nonlinear equations with less nonlinearity could be solved via numerical method, and therefore the numerical method converges more rapidly to the answer. Finally two different sets of singularity points with different natures are obtained.
Volume 2: 32nd Mechanisms and Robotics Conference, Parts A and B, 2008