Study on Dynamics Model of Macro/Micro Mechanical Arm of the New Workover

2012 ◽  
Vol 538-541 ◽  
pp. 1002-1005
Author(s):  
Yan Wang ◽  
Yu Lian Chang ◽  
Sheng Gao ◽  
Jing Wang
Keyword(s):  
Rigid Body ◽  
Mathematical Models ◽  
Rate Equation ◽  
Theoretical Basis ◽  
Equations Of Motion ◽  
Kinematics And Dynamics ◽  
Dynamics Analysis ◽  
Dynamics Model ◽  
Constraint Equations ◽  
Working Principle

Macro/micro mechanical arm is an important component of workover mechanical system. According to its composition characteristics and working principle, the arm was simplified to a plane system that all components were working in the same plane. Based on rigid body kinematics and dynamics theories, the kinematics and dynamics mathematical models of arm lifting progress were established by using constraint equations, rate equation, acceleration equations, virtual principle work, lagrange multiplier and differential-algebraic mixed equations of motion. It provides theoretical basis for kinematics and dynamics analysis of the macro/micro mechanical arm in lifting process.

Dynamics Analysis of A Planetary Mechanism Soft Starter

2011 ◽  
Vol 86 ◽  
pp. 247-251
Author(s):  
Xue Jiang ◽  
Ji Hua Bao ◽  
Yuan Zhang ◽  
Yan Yu
Keyword(s):  
System Dynamics ◽  
Theoretical Basis ◽  
Constant Load ◽  
Disc Brake ◽  
Dynamics Analysis ◽  
Brake Torque ◽  
Uniform Acceleration ◽  
Soft Starter ◽  
Working Principle ◽  
Planetary Mechanism

For studying controlling tragedy of soft starter with disc brake, its working principle was analyzed, and system dynamics equation was established. Besides, the brake torque provided by the disc brake was counted. The analysis indicates that, for the constant load starting in uniform acceleration, the brake oil-pressure must keep invariable. The conclusions provide theoretical basis for the hydraulic and electrical controlling of soft starter.

Dynamics Analysis of a Sinking Winch Mechanism

2011 ◽  
Vol 105-107 ◽  
pp. 454-457
Author(s):  
Xing Guo Shao ◽  
Zhen Cai Zhu ◽  
Guo Hua Cao ◽  
Yi Lei Li
Keyword(s):  
Numerical Simulation ◽  
Dynamic Analysis ◽  
Lagrange Multiplier ◽  
Simulation Study ◽  
Equations Of Motion ◽  
Dynamics Analysis ◽  
Unilateral Constraints ◽  
Dynamics Model ◽  
Midpoint Method ◽  
Smooth Dynamics

This paper investigates the dynamics of a sinking winch mechanism in the framework of non-smooth dynamics. The previous works ignored the unilateral property of the cable (it can only pull the platform but can’t push it), which is specially taken into consideration in this paper. We propose the set-valued tension law to model the unilateral constraints of the cables. The equations of motion are derived by use of the Lagrange multiplier method. The dynamics model of the mechanism is obtained by combining the equations of motion and the set-valued tension law. Its solution is solved by the Moreau midpoint method. We present a numerical simulation study to demonstrate that the non-smooth dynamics framework is effective and suitable for the dynamic analysis of the sinking winch mechanism.

Dynamic Modeling and Simulation of Flexible Robots With Prismatic Joints

1990 ◽  
Vol 112 (3) ◽  
pp. 307-314 ◽  
Author(s):  
Ye-Chen Pan ◽  
R. A. Scott ◽  
A. Galip Ulsoy
Keyword(s):  
Rigid Body ◽  
Equations Of Motion ◽  
Numerical Procedure ◽  
Differential Algebraic Equations ◽  
Rigid Body Motion ◽  
Body Motion ◽  
Integration Scheme ◽  
System Response ◽  
Constraint Equations ◽  
Prismatic Joints

A dynamic model for flexible manipulators with prismatic joints is presented in Part I of this study. Floating frames following a nominal rigid body motion are introduced to describe the kinematics of the flexible links. A Lagrangian approach is used in deriving the equations of motion. The work done by the rigid body axial force through the axial shortening of the link due to transverse deformations is included in the Lagrangian function. Kinematic constraint equations are used to describe the compatibility conditions associated with revolute joints and prismatic joints, and incorporated into the equations of motion by Lagrange multipliers. The small displacements due to the flexibility of the links are then discretized by a displacement based finite element method. Equations of motion are derived for the cases of prescribed rigid body motion as well as prescribed joint torques/forces through application of Lagrange’s equations. The equations of motion and the constraint equations result in a set of differential algebraic equations. A numerical procedure combining a constraint stabilization method and a Newmark direct integration scheme is then applied to obtain the system response. An example, previously treated in the literature, is presented to validate the modeling and solution methods used in this study.

scholarly journals SIMULATION OF ANTHROPOMORPHIC ROBOTS WITH ELASTIC DRIVES BY INTRODUCING VIRTUAL LINKS

2018 ◽  
Vol 22 (3) ◽  
pp. 59-66
Author(s):  
S. I. Savin ◽  
L. Yu. Vorochaeva
Keyword(s):  
Mathematical Models ◽  
Control Systems ◽  
Sagittal Plane ◽  
Equations Of Motion ◽  
Bipedal Walking ◽  
Walking Robots ◽  
Structure And Properties ◽  
Dynamics Model ◽  
Sit To Stand ◽  
Virtual Links

Anthropomorphic walking robots are among the most promising robot types, due to the possibility to introduce them into the urbane environment through the use of the existing infrastructure. Control systems developed for such robots require access to the exact mathematical models of these robots, taking into account the properties of actuators, gears and sensors. In this paper, we consider approaches to describing the model of a bipedal walking robot with elastic drives. The robot is a three-link mechanism that moves in the sagittal plane and performs verticalization (sit-to-stand transfer). Two variants of describing the dynamics of the robot are shown. In the first variant, the number of equations describing the movement of the robot is doubled due to the introduction of elastic drives, in comparison with the case when there are no elastic elements present. In the second variant, there is robot model and the elastic element dynamics model, and bothare described separately. The advantages of this method include the fact that it allows us to preserve the structure and properties of the equations of motion of the mechanism used in constructing control methods in cases when the elastic properties of the gears are not taken into account, and it also allows to conserve the structure of the generalized inertia matrix. The simulation results are presented in two described previously variants, their comparison is made. It is established that both mathematical models behave almost identically, with the most significant differences manifested in the formation of control actions generated by the regulator.

A New Order-N Order-N3 Hybrid Parallelizable Algorithm for a Multi-Rigid-Body Mechanical System

1999 ◽  
Author(s):  
Kurt S. Anderson ◽  
Shanzhong Duan
Keyword(s):  
Rigid Body ◽  
State Space ◽  
Mechanical System ◽  
Equations Of Motion ◽  
Parallel System ◽  
Body Motion ◽  
System Model ◽  
New Order ◽  
Constraint Equations ◽  
Floating Base

Abstract In this paper, a new hybrid parallelizable algorithm involving formulations of different computational orders is presented for chain systems. The parallel system model is constructed through the separation of certain system interbody joints so that largely independent multibody subchain systems are formed. These sub-chains in turn interact with one another through associated unknown constrain forces fc¯ at those separated joints. Within each of the floating subchains, equations of motion for the system of bodies are produced using a recursive state space O(n) formulation, while the equations associated specifically with the floating “composite” base body are formed using a more tradition O(n3) approach. Parallel strategies are used to form and solve constraint equations between subchains concurrently. 41% computational savings can be achieved for the floating base body motion description by using O(n3) approach relative to using sequential O(n) procedure.

scholarly journals Closed-form time derivatives of the equations of motion of rigid body systems

2021 ◽  
Author(s):  
Andreas Müller ◽  
Shivesh Kumar
Keyword(s):  
Rigid Body ◽  
Closed Form ◽  
Multibody Systems ◽  
Equations Of Motion ◽  
Alternative Formulation ◽  
Dynamics Of Rigid Body ◽  
Control Forces ◽  
And Control ◽  
Derivatives Of ◽  
Insight Into

AbstractDerivatives of equations of motion (EOM) describing the dynamics of rigid body systems are becoming increasingly relevant for the robotics community and find many applications in design and control of robotic systems. Controlling robots, and multibody systems comprising elastic components in particular, not only requires smooth trajectories but also the time derivatives of the control forces/torques, hence of the EOM. This paper presents the time derivatives of the EOM in closed form up to second-order as an alternative formulation to the existing recursive algorithms for this purpose, which provides a direct insight into the structure of the derivatives. The Lie group formulation for rigid body systems is used giving rise to very compact and easily parameterized equations.

scholarly journals Mathematical models of supersonic and intersonic crack propagation in linear elastodynamics

2021 ◽  
Author(s):  
Javier Bonet ◽  
Antonio J. Gil
Keyword(s):  
Kinetic Energy ◽  
Crack Propagation ◽  
Mathematical Models ◽  
Linear Elasticity ◽  
Strain Energy ◽  
Equations Of Motion ◽  
Two Dimensions ◽  
Discontinuous Solutions ◽  
Linear Elasticity Theory ◽  
Intersonic Crack Propagation

AbstractThis paper presents mathematical models of supersonic and intersonic crack propagation exhibiting Mach type of shock wave patterns that closely resemble the growing body of experimental and computational evidence reported in recent years. The models are developed in the form of weak discontinuous solutions of the equations of motion for isotropic linear elasticity in two dimensions. Instead of the classical second order elastodynamics equations in terms of the displacement field, equivalent first order equations in terms of the evolution of velocity and displacement gradient fields are used together with their associated jump conditions across solution discontinuities. The paper postulates supersonic and intersonic steady-state crack propagation solutions consisting of regions of constant deformation and velocity separated by pressure and shear shock waves converging at the crack tip and obtains the necessary requirements for their existence. It shows that such mathematical solutions exist for significant ranges of material properties both in plane stress and plane strain. Both mode I and mode II fracture configurations are considered. In line with the linear elasticity theory used, the solutions obtained satisfy exact energy conservation, which implies that strain energy in the unfractured material is converted in its entirety into kinetic energy as the crack propagates. This neglects dissipation phenomena both in the material and in the creation of the new crack surface. This leads to the conclusion that fast crack propagation beyond the classical limit of the Rayleigh wave speed is a phenomenon dominated by the transfer of strain energy into kinetic energy rather than by the transfer into surface energy, which is the basis of Griffiths theory.

scholarly journals Kinematics and Dynamics Analysis of a 3-DOF Upper-Limb Exoskeleton with an Internally Rotated Elbow Joint

2018 ◽  
Vol 8 (3) ◽  
pp. 464 ◽  
Author(s):  
Xin Wang ◽  
Qiuzhi Song ◽  
Xiaoguang Wang ◽  
Pengzhan Liu
Keyword(s):  
Upper Limb ◽  
Elbow Joint ◽  
Kinematics And Dynamics ◽  
Dynamics Analysis ◽  
Upper Limb Exoskeleton

Systematic Construction of the Equations of Motion for Multibody Systems Containing Closed Kinematic Loops

1989 ◽  
Author(s):  
P. E. Nikravesh ◽  
G. Gim
Keyword(s):  
Equations Of Motion ◽  
Transformation Matrix ◽  
Velocity Transformation ◽  
Constraint Equations ◽  
Advantages And Disadvantages ◽  
Lagrange Multiplier Technique ◽  
Joint Coordinates ◽  
Minimum Number ◽  
Kinematic Loops ◽  
Equations Of Motions

Abstract This paper presents a systematic method for deriving the minimum number of equations of motion for multibody system containing closed kinematic loops. A set of joint or natural coordinates is used to describe the configuration of the system. The constraint equations associated with the closed kinematic loops are found systematically in terms of the joint coordinates. These constraints and their corresponding elements are constructed from known block matrices representing different kinematic joints. The Jacobian matrix associated with these constraints is further used to find a velocity transformation matrix. The equations of motions are initially written in terms of the dependent joint coordinates using the Lagrange multiplier technique. Then the velocity transformation matrix is used to derive a minimum number of equations of motion in terms of a set of independent joint coordinates. An illustrative example and numerical results are presented, and the advantages and disadvantages of the method are discussed.

A Hybrid Highly Parallelizable Algorithm for the Dynamics of Rigid Body Chain Systems

1999 ◽  
Author(s):  
Shanzhong Duan ◽  
Kurt S. Anderson
Keyword(s):  
Rigid Body ◽  
Degrees Of Freedom ◽  
High Efficiency ◽  
Equations Of Motion ◽  
Constraint Forces ◽  
Dynamics Of Rigid Body ◽  
A Chain ◽  
Explicit Determination ◽  
Order Algorithm

Abstract The paper presents a new hybrid parallelizable low order algorithm for modeling the dynamic behavior of multi-rigid-body chain systems. The method is based on cutting certain system interbody joints so that largely independent multibody subchain systems are formed. These subchains interact with one another through associated unknown constraint forces f¯c at the cut joints. The increased parallelism is obtainable through cutting the joints and the explicit determination of associated constraint loads combined with a sequential O(n) procedure. In other words, sequential O(n) procedures are performed to form and solve equations of motion within subchains and parallel strategies are used to form and solve constraint equations between subchains in parallel. The algorithm can easily accommodate the available number of processors while maintaining high efficiency. An O[(n+m)Np+m(1+γ)Np+mγlog2Np](0<γ<1) performance will be achieved with Np processors for a chain system with n degrees of freedom and m constraints due to cutting of interbody joints.

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