Dynamics and Control of Multi-Flexible-Body Systems in a Divide-and-Conquer Scheme

2015 ◽  
Author(s):  
Imad M. Khan ◽  
Kalyan C. Addepalli ◽  
Mohammad Poursina
Keyword(s):  
Inverse Dynamics ◽  
Equations Of Motion ◽  
Divide And Conquer ◽  
Flexible Body ◽  
Constraint Forces ◽  
Control Laws ◽  
Motion Constraints ◽  
Divide And Conquer Algorithm ◽  
Dynamics And Control ◽  
Kinematic Loops

In this paper, we present an extension of the generalized divide-and-conquer algorithm (GDCA) for modeling constrained multi-flexible-body systems. The constraints of interest in this case are not the motion constraints or the presence of closed kinematic loops but those that arise due to inverse dynamics or control laws. The introductory GDCA paper introduced an efficient methodology to include generalized constraint forces in the handle equations of motion of the original divide-and-conquer algorithm for rigid multibody systems. Here, the methodology is applied to flexible bodies connected by kinematic joints. We develop necessary equations that define the algorithm and present a well known numerical example to validate the method.

Multi-Flexible-Body Simulations Using Interpolating Splines in a Divide-and-Conquer Scheme

2013 ◽  
Author(s):  
Imad M. Khan ◽  
Woojin Ahn ◽  
Kurt Anderson ◽  
Suvranu De
Keyword(s):  
Equations Of Motion ◽  
Linear Equations ◽  
Divide And Conquer ◽  
Flexible Body ◽  
Divide And Conquer Algorithm ◽  
Large Rotations ◽  
Floating Frame ◽  
Interpolating Splines ◽  
Divide And Conquer Scheme ◽  
Logarithmic Complexity

A new method for modeling multi-flexible-body systems is presented that incorporates interpolating splines in a divide-and-conquer scheme. This algorithm uses the floating frame of reference formulation and piece-wise interpolation spline functions to construct and solve the non-linear equations of motion of the multi-flexible-body systems undergoing large rotations and translations. We compare the new algorithm with the flexible divide-and-conquer algorithm (FDCA) that uses the assumed modes method and may resort to sub-structuring in many cases [1]. We demonstrate, through numerical examples, that in such cases the interpolating spline-based approach is comparable in accuracy and superior in efficiency to the FDCA. The algorithm retains the theoretical logarithmic complexity inherent to the divide-and-conquer algorithm when implemented in parallel.

Computed Torque Control of Articulated Multibody Systems in the Generalized Divide and Conquer Algorithm Framework

2015 ◽  
Author(s):  
Cameron Kingsley ◽  
Mohammad Poursina
Keyword(s):  
Multibody Systems ◽  
Inverse Dynamics ◽  
Equations Of Motion ◽  
Torque Control ◽  
Divide And Conquer ◽  
Controlled System ◽  
Divide And Conquer Algorithm ◽  
Computed Torque Control ◽  
And Control ◽  
Computed Torque

An extension to the Generalized-Divide-and-Conquer Algorithm (GDCA) is presented in this paper in conjunction with the Computed-Torque-Control-Law (CTCL) to model and control fully actuated multibody systems. CTCL uses the inverse dynamics to provide control inputs to the system while, the dynamics of the system must be formed and solved in each iteration. Herein, the GDCA is extended to form and solve the inverse dynamics to find control torques. Further, this method is also extended to efficiently solve the equations of motion of the controlled system. This significantly reduces the complexity of modeling, simulating, and controlling the fully actuated multibody systems to O(n) or O(logn) operations in each iteration in the serial and parallel implementations, respectively.

Generalized Orthogonal Complement Based Divide and Conquer Algorithm for Constrained Multibody Dynamics

2009 ◽  
Author(s):  
Rudranarayan M. Mukherjee ◽  
Kurt S. Anderson
Keyword(s):  
Equations Of Motion ◽  
Divide And Conquer ◽  
Orthogonal Complement ◽  
Assembly Process ◽  
Short Article ◽  
Current Form ◽  
Divide And Conquer Algorithm ◽  
Constrained Multibody Dynamics ◽  
Kinematic Loops ◽  
Generalized Orthogonal

This paper presents an extension of the orthogonal complement based divide and conquer algorithm for constraint multi-rigid body systems containing closed kinematic loops in generalized topologies. In its current form, its a short article demonstrating the methodology for assembling the equations of motion in a hierarchic assembly process for systems containing multiple loops in generalized topologies.

Multibody Dynamics in Generalized Divide and Conquer Algorithm (GDCA) Scheme

2011 ◽  
Author(s):  
Mohammad Poursina ◽  
Kurt S. Anderson
Keyword(s):  
Multibody Systems ◽  
Inverse Dynamics ◽  
Original System ◽  
Parent Body ◽  
Divide And Conquer ◽  
Loop Control ◽  
Generalized Coordinates ◽  
Divide And Conquer Algorithm ◽  
Generalized Force ◽  
New Formulation

Generalized divide and conquer algorithm (GDCA) is presented in this paper. In this new formulation, generalized forces appear explicitly in handle equations in addition to the spatial forces, absolute and generalized coordinates which have already been used in the original version of DCA. To accommodate these generalized forces in handle equations, a transformation is presented in this paper which provides an equivalent spatial force as an explicit function of a given generalized force. Each generalized force is then replaced by its equivalent spatial force applied from the appropriate parent body to its child body at the connecting joint without violating the dynamics of the original system. GDCA can be widely used in multibody problems in which a part of the forcing information is provided in generalized format. Herein, the application of the GDCA in controlling multibody systems in which the known generalized forces are fedback to the system is explained. It is also demonstrated that in inverse dynamics and closed-loop control problems in which the imposed constraints are often expressed in terms of generalized coordinates, a set of unknown generalized forces must be considered in the dynamics of system. As such, using both spatial and generalized forces, GDCA can be widely used to model these complicated multibody systems if it is desired to benefit from the computational advantages of the DCA.

Orthogonal Complement-Based Divide and Conquer Algorithm: A Detailed Investigation of Its Performance

2013 ◽  
Author(s):  
Imad M. Khan ◽  
Kurt S. Anderson
Keyword(s):  
Growth Rate ◽  
Arbitrary Number ◽  
Multibody Systems ◽  
Divide And Conquer ◽  
Orthogonal Complement ◽  
Error Growth ◽  
Stabilization Method ◽  
Constraint Violation ◽  
Divide And Conquer Algorithm ◽  
Kinematic Loops

In this paper, we characterize the orthogonal complement-based divide-and-conquer (ODCA) [1] algorithm in terms of the constraint violation error growth rate and singularity handling capabilities. In addition, we present a new constraint stabilization method for the ODCA architecture. The proposed stabilization method is applicable to general multibody systems with arbitrary number of closed kinematic loops. We compare the performance of the ODCA with augmented [2] and reduction [3] methods. The results indicate that the performance of the ODCA falls between these two traditional techniques. Furthermore, using a numerical example, we demonstrate the effectiveness of the new stabilization scheme.

Efficient Large Deformation Simulations of Multi-Flexible-Body Systems Using Absolute Nodal Coordinate Beam and Plate Elements

2014 ◽  
Author(s):  
Imad M. Khan ◽  
Kurt S. Anderson
Keyword(s):  
Absolute Nodal Coordinate Formulation ◽  
Divide And Conquer ◽  
Flexible Body ◽  
Elastic Deformations ◽  
Absolute Nodal Coordinate ◽  
Numerical Examples ◽  
Divide And Conquer Algorithm ◽  
Plate Elements ◽  
The Absolute ◽  
The Individual

In this paper, we investigate the absolute nodal coordinate finite element (FE) formulations for modeling multi-flexible-body systems in a divide-and-conquer framework. Large elastic deformations in the individual components (beams and plates) are modeled using the absolute nodal coordinate formulation (ANCF). The divide-and-conquer algorithm (DCA) is utilized to model the constraints arising due to kinematic joints between the flexible components. We develop necessary equations of the new algorithm and present numerical examples to test and validate the method.

Inverse dynamics of the 6-dof out-parallel manipulator by means of the principle of virtual work

Robotica ◽  
2009 ◽  
Vol 27 (2) ◽  
pp. 259-268 ◽  
Author(s):  
Yongjie Zhao ◽  
Feng Gao
Keyword(s):  
Parallel Manipulator ◽  
Inverse Dynamics ◽  
Virtual Work ◽  
Equations Of Motion ◽  
Principle Of Virtual Work ◽  
Constraint Forces ◽  
Dynamical Equations ◽  
Robot System ◽  
Lead Screw ◽  
Moving Platform

SUMMARYIn this paper, the inverse dynamics of the 6-dof out-parallel manipulator is formulated by means of the principle of virtual work and the concept of link Jacobian matrices. The dynamical equations of motion include the rotation inertia of motor–coupler–screw and the term caused by the external force and moment exerted at the moving platform. The approach described here 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. Numerical simulation for the inverse dynamics of a 6-dof out-parallel manipulator is illustrated. The whole actuating torques and the torques caused by gravity, velocity, acceleration, moving platform, strut, carriage, and the rotation inertia of the lead screw, motor rotor and coupler have been computed.

New and Extended Applications of the Divide-and-Conquer Algorithm for Multibody Dynamics

2014 ◽  
Vol 9 (4) ◽  
Author(s):  
Jeremy J. Laflin ◽  
Kurt S. Anderson ◽  
Imad M. Khan ◽  
Mohammad Poursina
Keyword(s):  
Multibody Dynamics ◽  
Large Deformations ◽  
Multibody System ◽  
Divide And Conquer ◽  
Flexible Body ◽  
Ongoing Research ◽  
Flexible Bodies ◽  
Computational Burden ◽  
Divide And Conquer Algorithm ◽  
Model Fidelity

This work presents a survey of the current and ongoing research by the authors who use the divide-and-conquer algorithm (DCA) to reduce the computational burden associated with various aspects of multibody dynamics. This work provides a brief discussion of various topics that are extensions of previous DCA-based algorithms or novel uses of this algorithm in the multibody dynamics context. These topics include constraint error stabilization, spline-based modeling of flexible bodies, model fidelity transitions for flexible-body systems, and large deformations of flexible bodies. It is assumed that the reader is familiar with the “Advances in the Application of the DCA to Multibody System Dynamics” text as the notation used in this work is explained therein and provides a summary of how the DCA has been used previously.

scholarly journals Principal vectors and equivalent mass descriptions for the equations of motion of planar four-bar mechanisms

2019 ◽  
Vol 48 (3) ◽  
pp. 259-282
Author(s):  
J. P. Meijaard ◽  
V. van der Wijk
Keyword(s):  
Virtual Work ◽  
Mass Matrix ◽  
Equations Of Motion ◽  
Euler Method ◽  
Constraint Forces ◽  
Equivalent Mass ◽  
Kinematic Loops ◽  
Principal Points ◽  
Kinematic Loop ◽  
Four Bar Linkage

AbstractThe use of principal points and principal vectors in the formulation of the equations of motion of a general 4R planar four-bar linkage is shown with two kinds of methods, one that opens kinematic loops and one that does not. The opened kinematic loop approach analyses the moving links as a system with a tree connectivity, introducing reaction forces for closing the loops. Compared with the conventional Newton–Euler method, this approach results in fewer equations and constraint forces, whereas the mass matrix entries remain meaningful, but there is a stronger coupling between the equations. Two equivalent mass formulations for the closed kinematic loop approach are presented, which need not open the loop and introduce loop constraint forces in the equations of motion. With the method of complex joint masses, the mass of the links closing the loops is represented by real and virtual equivalent masses, defining the principal points. The principle of virtual work with the inclusion of inertia terms is used to derive the equations of motion. As an example the dynamic balance conditions of the four-bar linkage are derived. With the method of the equivalent mass matrix it is shown how a constant mass matrix can be used to describe the dynamics of binary links with an arbitrary mass distribution. A four-bar linkage could be modelled with only three truss elements instead of the conventional result with three or more beam elements, which gives a significant reduction of the computational complexity.

Sign in / Sign up

Export Citation Format

Share Document