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This research presents a dynamic analysis of a large-scale hydraulic cylinder actuator via numerical simulation. A model of the actuator built with dynamically parameters is implemented basing on fluid mechanics and vibration theories. In which, coefficients of viscous damping and stiffness generated by compressibility and viscous characteristics of hydraulic oil are considered. Hence, the large-scale hydraulic cylinder actuator can be investigated via an equivalent model of mass-spring-damper. In order of obtaining the system response, numerical simulation is done with some realistic actuator parameter sets. The results are consistent with reality and can be used as valuable fundamental for large-scale hydraulic cylinder actuator design.

The uncertainty of mechanical system performance is strongly influenced by the properties of system components such as mass, stiffness-damping coefficient, and friction coefficient. Based on computational simulations, the system performance under uncertainty conditions can be estimated. However, the nonlinear dynamic behavior of friction is difficult to simulate in numerical simulations, this research is therefore employed a smooth stick-slip friction force model instead of the Coulomb friction force model. Monte Carlo simulation (MCS) combined with multibody dynamic (MBD) simulation is proposed to evaluate the uncertainty characteristics of the system components and stick-slip friction force between two contacting bodies. Numerical simulations applied the proposed method were performed to consider the effects of uncertainty of friction coefficient on the machining accuracy of a three axes CNC (Computer Numerical Control) machine tool.

The simulation and application of industrial robots has developed very quickly in recent decades. Along with the development of computer science, a lot of softwares to perform dynamic simulation have been created. The results of simulation can be used for layout evaluation, kinematic, dynamic study, off-line programming to avoid obstacle and for design mechanical structure of robots. A co-simulation of 2R industrial robots have been performed by Recurdyn and Matlab. The input parameters are executed under Matlab, and then exported to Recurdyn environment. Kinematic parameters will be executed by RecurDyn then exported to Matlab. The main tasks of this paper are performing 2R robotic manipulator kinematic simulation in two postures with the same trajectory and the same time. Thus, the result of simulation can be compared with theories. Finally, a real 2R robot model was used to verify the trajectory with CAE simulation.

The purpose of this paper is to investigate the effect of friction on two wheels vehicle control. First, the two wheels vehicle model is presented. Then, the dynamic analysis are performed by studying the dynamic of inverted pendulum. The PID control is used as the control method to control motor for balancing two wheels vehicle. Furthermore, the numerical modeling is created and the friction is given on joint with varying the coefficient of friction in numerical simulation. Moreover, the optimize PID value is presented and then the numerical simulation is performed.

This research presents a numerical analysis of hydraulic actuator dynamics considering the effect of elastic material components. A hydraulic position control is established with dynamically parameters basing on mechanic theories. In which, coefficients of viscous damping, stiffness of hydraulic oil and friction of polymer seals are considered. Hence, the model can be analyzed as a mass-spring-damper system. This research employs numerical simulation for obtaining system dynamic responses. The results are consistent with theories and reality. These are useful in design and calculations of hydraulic control systems.

This research performs finite element simulations of cracked structures undergoing the vibrothermography process, which is an experimental technique gaining popularity for structural damage identification. In vibrothermography, a vibration shaker is used to excite the test structure. If the structure has cracks or defects, frictional heat will be generated at those cracks and thermal images can be recorded by an infrared camera. The vibrothermographical simulation includes modal analysis, transient vibration and transient thermal analysis. Two simulated examples are presented in this work: the first one is an aluminum-alloy plate with a hairline crack; the second example is a brake rotor with a hairline crack on one of the bolt-hole surfaces. Although higher modes are usually more difficult to excite, they may be used in vibrothermography to detect structural cracks more efficiently.

The main objective of this research is to propose a multidisciplinary approach for the development and design of Computer Numerical Control (CNC) machine tools using numerical optimization methods combined Multi-Body Dynamic (MBD) analysis and to control design co-simulation. Metamodels based Sequential Approximate Optimization (SAO) for the co-simulation optimization problems are developed. The metamodels are constructed as approximate models for exact dynamic analysis responses by using simultaneous Kriging metamodeling method. SAO problems for single objective and multi-objective optimization designs are carried out based on the augmented Lagrange multiplier (ALM) method. An application of the proposed method on optimizing Proportional-Integral-Derivative (P-I-D) coefficients of PID controllers of a CNC machine tool model is performed to demonstrate the usefulness of integrating different research methods in numerical simulation. Therefore, this work overcomes a difficult task in tuning the PID controller which requires extensive experience and understandings of research and development (R&D) engineers. Moreover, the optimal PID controllers obtained by the multidisciplinary approach can help to increase the contouring accuracy of the CNC machine tools.

Purpose The purpose of this paper is to study the influence of friction on static and dynamic characteristics, as well as the strength and lifetime of a flexible three-axes computer numerical control (CNC) machine tool. Design/methodology/approach The machine tool is first modeled by using finite element method to analyze static structure with frictionless surface-to-surface contact type. Because the machine tool structure is becoming more and more sophisticated over time, the significant influence of contact conditions between structural elements on the dynamic characteristics of the whole structure must be considered. To examine the dynamic effects caused by inertia forces and displacement of moving bodies on contact stress, the coefficient of friction between two contact bodies is added to perform dynamic simulation and compare the results with the static analysis results. Findings Distribution of stress and contact forces in solid-flexible contact is also studied by using the fundamental dynamic characteristics of a bushing joint. Originality/value Finally, the influence of dynamic structure, cutting conditions and material properties on the strength and lifetime of the CNC machine tool is discussed by using fatigue analysis. Consequently, this research can be used for efficient simulation of structural dynamics, lifetime assessment and interactions of the real CNC machine with the machine tool structure in a virtual environment.

Robot simulation has developed quickly in recent decades. Along with the development of computer science, a lot of simulation soft-wares have been created to perform many purposes such as studying kinematic, dynamic, and off-line program to avoid obstacle on manipulator robots. The main objective of this study is therefore to analyze kinematic, dynamic characteristics of an R-R robotic manipulator in order to control this robot. Newton-Euler method was used to calculate the torque acting on each joint of the robot. Then, a numerical model of the robot was established by a multi-body dynamics software to compare with the results obtained by Newton-Euler theory. After that, a feed-forward control system was created by RecurDyn/CoLink to control the end-effector of the robot following a desired trajectory. The results showed that this research can be used for efficient simulation of structural kinematics, dynamics as well as control of the real manipulator robot with the robot structure in a virtual environment.

Dynamic control on hydraulic machine system and kinematic control on industrial robotic manipulators are two studied topics in this research. The main objective of this study is to analyze dynamic, forward kinematic and inverse kinematic on a couple of mechanical systems and hydraulic mechanical systems in order to control these machines. The characteristics of hydraulic and manipulator robot parameters are firstly calculated by using dynamic theories. In the former topic, we perform an example on CNC machine tools which is designing a hydraulic controller to move a cutting tool along a circular path. Dynamics analysis, forward kinematics and inverse kinematics of industrial robotic are archived in the latter topic. Two experiments were also performed on RRR and RRRRRR manipulators by analyzing the inverse kinematic equations to make these robots follow the desired trajectories. This study takes innovations and achieves control improvement in different systems with optimization controller or trajectory planning.

In this paper, the influence of friction on static, dynamic characteristics, the strength and lifetime of a 3-axes flexible CNC machine tool are taken into account. The machine tool is first modelled by using finite element method (FEM) to perform static structural analysis. After that, the dynamic effects caused by the inertia forces and the displacement of moving part of the machine on contact stress are considered in this study. Then, the stress and contact force distributions on solid-flexible contact are also obtained. Finally, the influence of dynamic structure, cutting conditions and material properties on strength and lifetime of CNC machine tool are discussed by using fatigue analysis. Consequently, the proposed method can be used for efficient simulation of structural dynamics, lifetime assessment as well as interactions of the real CNC machine with the machine tool structure in a virtual environment.

This research introduced meta-models based Design For Six Sigma (DFSS) and robust design optimization (RDO) for dynamic performance optimization problems, which could eliminate the design sensitivity analysis (DSA) and deal with numerical noises. The optimization methodologies could be executed effortlessly based on the gradient information of meta-models, robust/DFSS optimization combined with meta-models was therefore proposed to optimize shape of mechanical structures and gain coefficients of proportional-integral-derivative (PID) controller for multi-body systems (MBS). Meta-model based on simultaneous Kriging method was first presented to construct approximate models for optimization design objectives. Then, robust/DFSS design optimization formulation was also described in this paper. Two numerical examples on shape optimization with a flexible cantilever beam model and the gain value optimization of PID control algorithm with an inverted-pendulum model were performed to demonstrate the proposed optimization method. The former example described structural optimization of a flexible body under dynamic loading conditions within an MBS approach. In the latter example, the optimal values of P, I, D gains were obtained by using co-simulation between multibody dynamic (MBD) analysis and control environment. Therefore, this study achieved structural and control design improvement in different systems with the optimization theories.

This paper presents simulation of multibody manufacturing systems with the support of numerical tools. The dynamic and cybernetic characteristics of driving system are discussed. Simple prototype models of robot arm and machine tool’s driving system are quickly established in Computer Aided Design (CAD) software inwhich the whole specification of material, inertia and so on are involved. The prototypes therefore are simulated in RecurDyn- a Computer Aided Engineering (CAE) software. The models are driven by controllers built in Matlab/Simulink via co-simulation. The results are suitable with theory and able to exploied for expansion of complexly effective factors. The research indicates that dynamic analysis and control could be done via numerical method instead of directly dynamic equation creation for multibody manufacturing systems.

In this paper, a synchronous approach for dynamic simulation of machine tools is described. Computer Aided Engineering (CAE) method models and analyzes a dynamical parameter prototype of machine tools. In which, the flexible structure, interactive movement, non-linear factor effects as well as characteristics of resonance frequencies and mechanical transfer function are considered. The integrating Finite Element Method (FEM), Multi-Body Dynamics (MBD) and control carries out a solution of machine tools simulation for predicting dynamic machine behaviors. The static analysis and modal analysis of components are presented with sample examples. Cybernetic characteristics like Bode diagram and such a controller are implemented for movement tailors. The synchronous approach deduces a practically technical method for machines tools.

The main objective of this paper is to provide the methods and techniques to improve the design and manufacturing ability of electric scooter. The loads of some structure parts and the steering mechanism of the electric scooter are analyzed with RecurDyn. The stress distribution of steering mechanism and transmission mechanism can be calculated and performed with finite element analysis software. By using the computational ability and simulation of modern computer softwares, the factor of material fatigue can be found. The results of this research can be used to improve the design of electric scooter in the future.

Circular diamond saws rotating in high speed are widely used to cut hard materials, and narrow slots on saw blades are sometimes used to reduce the blades vibration and noise. Sizing optimization of the annular slots on saw blades is investigated in this paper. First, an accurate finite element model representing an actual saw blade is obtained by model updating. Then, sizing optimization on two types of annular slots is performed to maximize the frequency separation between the finite element analysis results and the saw blades operational speed, and to reduce the possibility of structural resonance. Optimization results demonstrate great improvements in frequency separation from the rotating speed of 500 Hz for the optimized models.

The main objective of this paper is to simulate the mobility of humanoid robot. Simulation method implemented by using RecurDyn, one can analyze the kinematics and dynamics of BIOLOID humanoid robot. Moreover, the analysis of mobility will be discussed. In this paper, the Zero-Moment Point and Forward Dynamics methods are also introduced to the dynamic analysis of humanoid robot. Finally, the simulation results show that the algorithms developed in this paper can efficiently enhance the stability of the humanoid robot.

In this paper, an analysis has been conducted to explore the momentun and thermal transport characterastics of electroosmotic liquid flow in a microchannel under imposed constant wall heat flux boundary condition. The present formulation shows that the problem is governed by three parameters, namely, the length scale ratio (ratio of Debye length to half channel height), the Joule heating parameter (ratio of Joule heating to surface heat flux), and the Brinkman number. A closed form solution of the problem was obtained and the impact of viscous dissipation on the heat transfer behavior was investigated. Analytical exact solutions of dimensionless velocity and temperature profiles, normalized local velocity, volume flow rate, friction coefficient, mean fluid temperature, and the fully-developed Nusselt number were obtained as functions of the governing parameters. Especially, the effects of length scale ratio on major flow parameters (including the normalized local velocity, friction coefficient, and volumetric flow rate) were examined. Also, the viscous dissipation effect on thermal transport characteristics was discussed in depth.

The scroll compressor has the conjugate motion of meshing by the fixed scroll and the planet scroll. Several kinds of geometrical curves can be adopted to form the scroll compressor profile such as involute of circle with variable and constant radius, algebraic spiral, and so on, to improve the performance of scroll compressor. This study proposes a new scroll profile design using elliptic involute and two-envelope method to create a new conjugate meshing scroll of variable cross section. The curve of the scroll section on both sides can be specified as an arbitrary mathematical function. First, the base scroll swept out by the central base circle. Next, the base circle translation path envelope of the planet scroll is moved by the basic involute curve. The base circle translation path envelope is the first envelope. The second envelope generated by the planet scroll conjugate profile is the fixed scroll. By using two-envelope method, the variety of conjugate scroll can be produce with the cross section and symmetrical variables for parametric design.

In this paper, two experimental techniques, Electronic Speckle Pattern Interferometry and Stroboscopic Interferometry, and two different finite element analysis packages are used to measure or to analyze the frequencies and mode shapes of a micromachined, cross-shaped torsion structure. Four sets of modal data are compared and shown having a significant discrepancy in their frequency values, although their mode shapes are quite consistent. Inconsistency in the frequency results due to erroneous inputs of geometrical and material parameters to the finite element analysis can be salvaged by applying the finite element model updating procedure. Two updating cases show that the optimization sequences converge quickly and significant improvements in frequency prediction are achieved. With the inclusion of the thickness parameter, the second case yields a maximum of under 0.4% in frequency difference, and all parameters attain more reliable updated values.

This paper proposes a method of the geometric design for a new conjugate tooth profiles based on the envelope theory and coordinate transformation method, the mathematical and geometric models for the conforming gears design are proposed. A comparison study on the dynamic contact stress with the involute gear drive is carried out in this work.

Generally speaking, the human biomechanical systems can be classified into two main groups: open-loop and closed-loop systems. In this investigation, the nonlinear recursive formulation is developed for the kinematic analysis of human biomechanical systems. The nonlinear generalized Newton-Euler equations are developed for flexible bodies that undergo large translational and rotational displacements. These equations are formulated in terms of a set of time invariant scalars, vectors and matrices that depend on the spatial coordinates as well as the assumed displacement fields, and these time invariant quantities represent the dynamic coupling between the rigid body motion and elastic deformation. The formulation to solve equations of motion for human biomechanical systems consisting of interconnected rigid and flexible bodies is presented in this paper.

This paper proposes a new type of rack-cutter can generates the circular and noncircular conjugate tooth profiles. Based on the envelope theory and coordinate transformation method, the mathematical and geometric models for the conforming rotors design are proposed. A selected smooth continuous curve equation can be assigned as the initial profile for the rack-cutter. Results from this research can be successfully applied to different kinds of tooth profile design of gerotor pumps and rotary machines.

Generally speaking, the flexible manufacturing systems can be classified into two main groups: open-loop and closed-loop systems. In this investigation, a recursive formulation is developed for the dynamic analysis of open-loop flexible manufacturing systems. The nonlinear generalized Newton-Euler equations are developed for rigid and deformable bodies that undergo large translational and rotational displacements. These equations are formulated in terms of a set of time invariant scalars, vectors and matrices that depend on the spatial coordinates as well as the assumed displacement fields, and these time invariant quantities represent the dynamic coupling between the rigid body motion and elastic deformation. The method to solve equations of motion for open-loop systems consisting of interconnected rigid and deformable bodies is presented in this paper. This method applies recursive method with the Newton-Euler method for deformable bodies to obtain a large, loosely coupled system equations of motion. The solution techniques used to solve for the system equations of motion can be more efficiently implemented in the modern computer systems. The algorithms presented in this paper are demonstrated by using cylindrical joints that can be easily extended to revolute, slider and rigid joints. The recursive formulation developed in this investigation is illustrated by a practical numerical example.

In this paper, the hydraulic control system design and dynamic analysis are considered in superior calculation efficiency based on Lagrangian method and fundamental laws for getting control algorithms to investigate about hydraulic system how to control hydraulic system and take hydraulic controller to the optimization. The systems built in dynamical parameters are associated hydraulic control system achieved with control parameters. And then, an interface is achieved. The relations between control parameters are obtained. The numerical tools are going to determine all kinematic parameters of bodies such as displacement, velocities, accelerations as well as reaction forces are responded. The AMESim and RecurDyn are used such Computer Aided Engineering (CAE) techniques to solve the numerical examples in this paper. Those examples will imply that the equation of motion based on Euler–Lagrange equation and characteristic effect of force is executable. Through results, we could achieve control improvement at different hydraulic systems.

In this paper, the computer computation of nonlinear combination methods in deformable multibody dynamics is described. The organization of the computer program, which is used to automatically construct and numerically solve the system of loosely coupled equations of motion expressed in terms of the Cartesian, Euler Angles and joint coordinates, is discussed. The main processor computer program consists of three main modules: constraint module, mass module and force module. The constraint module is used for the computation of the relationship among translational, rotational and joint accelerations. The mass module is used for the computation of the system mass matrix as well as the nonlinear Coriolis and centrifugal forces associated with the Cartesian, Euler Angles and modal coordinates. The force module is used to evaluate the generalized external and modal forces associated with the translational, rotational, joint and modal coordinates. Computational efficiency is achieved by taking advantage of the structure of the resulting sparse system of loosely coupled equations. Elimination of the modal coordinates leads to small number of equations that can be solved for joint accelerations. The joint and the modal accelerations are integrated forward in time using explicit numerical integration methods. The translational/rotational displacements and velocities can then be determined using the kinematic relationships. The multibody manipulator and the slider-crank mechanical systems are used as two examples to demonstrate the use of the computational procedure discussed in this paper. Copyright © 2010 John Wiley & Sons, Ltd.

This paper designs a desired zero moment point (ZMP) trajectory and creates a centre of mass (CoM) trajectory based on this ZMP, in order to solve the problem of generating nonlinear trajectories o...

In this paper the computer implementation of the nonlinear recursive formulation in multibody dynamics systems is described. The organization of the computer algorithm which is used to automatically construct and numerically solve the system of loosely coupled dynamic equations expressed in terms of the absolute and joint coordinates is discussed. The inertia projection schemes used in most existing recursive formulations for the dynamic analysis of deformable mechanisms lead to dense coefficient matrices in the equations of motion. Consequently, there are strong dynamic couplings between the joint and elastic coordinates. By using the inertia matrix structure of deformable mechanical systems and the fact that the joint reaction forces associated with the elastic coordinates do represent independent variables, a reduced system of equations whose dimension is dependent of the number of elastic degrees of freedom is obtained. This system can be solved for the joint accelerations as well as the joint reaction forces. The multibody flexible four-bar system is used as an example to demonstrate the use of the procedure discussed in this paper.

The recursive projection schemes used in most existing recursive methods for solid deformable structure dynamic problems in precision manufacturing systems lead to dense coefficient matrices in the acceleration equations and consequently there is a strong dynamic coupling between the joint and elastic coordinates. When the number of elastic degrees of freedom in engineering materials increases, the size of the coefficient matrix in the acceleration equations becomes large and consequently the use of these recursive methods for solving the joint and elastic accelerations becomes less efficient. This paper discusses the problems associated with the recursive projection schemes used in the existing recursive methods, and it is shown that decoupling the joint and elastic accelerations using the nonlinear recursive method requires the factorization of nonlinear matrices whose dimensions are independent of the number of elastic degrees of freedom of the multibody system. An amalgamated formulation that can be used to decouple the elastic and joint accelerations for different multibody manufacturing systems is then proposed. The use of the nonlinear recursive method developed in this paper is demonstrated using the open-loop and closedloop chains in precision manufacturing systems.

The aim of this paper is to develop an efficient method for decoupling joint and elastic accelerations, while maintaining the nonlinear inertia coupling between rigid body motion and elastic body deformation. Almost all of the existing recursive methods for analysis of flexible open-loop and closed-loop multibody mechanical systems lead to dense coefficient matrices in the equations of motion, and consequently there are strong dynamic couplings between the joint and elastic coordinates. When the number of elastic degrees of freedom increases, the size of the coefficient matrix in the equations of motion becomes large and unfortunately the use of these methods for solving for the joint and elastic accelerations becomes less efficient. This paper discusses the problems associated with the inertia projection schemes used in the existing recursive methods, and it is shown that decoupling the joint and elastic accelerations using these methods requires the factorization of nonlinear matrices whose dimensions depend on the number of elastic degrees of freedom of the system. An amalgamated method that can be used to decouple the elastic and joint accelerations is then proposed. In this amalgamated decoupling formulation, the relationships between the absolute, elastic, and joint variables and the generalized Newton–Euler equations are used to develop systems of loosely coupled equations that have sparse matrix structure. Utilizing the inertia matrix structure of flexible manufacturing systems and the fact that the joint reaction forces associated with the elastic coordinates do represent independent variables, a reduced system of equations whose dimension is dependent on the number of elastic degrees of freedom is obtained. This system can be solved for the joint accelerations as well as for the joint reaction forces. The application of the procedure developed in this paper is illustrated using flexible open-loop robotic manipulators and closed-loop crank-slider mechanical systems. Copyright © 2007 John Wiley & Sons, Ltd.

The aim of this paper is to develop non-linear recursive formulations for decoupling joint and elastic accelerations, while maintaining the non-linear inertia coupling between rigid body motion and elastic deformation in deformable mechanical systems. The inertia projection schemes used in most existing recursive formulations for the dynamic analysis of deformable mechanisms lead to dense coefficient matrices in the equations of motion. Consequently, there are strong dynamic couplings between the joint and elastic coordinates. When the number of elastic degrees of freedom increases, the size of the coefficient matrix in the equations of motion becomes large. Consequently, the use of these recursive formulations for solving the joint and elastic accelerations becomes less efficient. In this paper, the non-linear recursive formulations have been used to decouple the elastic and joint accelerations in deformable mechanical systems. The relationships between the absolute, elastic and joint variables and generalized Newton–Euler equations are used to develop systems of loosely coupled equations that have sparse matrix structure. By using the inertia matrix structure of deformable mechanical systems and the fact that joint reaction forces associated with elastic coordinates do represent independent variables, a reduced system of equations whose dimension is dependent of the number of elastic degrees of freedom is obtained. This system can be solved for the joint accelerations as well as for the joint reaction forces. The use of the approaches developed in this investigation is illustrated using deformable open-loop serial robot and closed-loop four-bar mechanical systems. Copyright © 2007 John Wiley & Sons, Ltd.

Generating nonlinear trajectories of walking patterns is one of the most important problems in stability a humanoid robot when it walks on different ground conditions. In order to solve this problem, a desired Zero Moment Point (ZMP) trajectory is firstly designed and then a Center of Mass (CoM) trajectory will be created based on this ZMP. Hence, the preview control formulation which follows the planned ZMP patterns while reducing the jerk (acceleration derivation) is considered to implement this trajectory. In this study, the walking pattern for bipedal robot is generated by using a cart-table model. The procedure of apply a preview controller to the cart-table model will be presented in this investigation. After that, the position of each leg joint of bipedal robot is also calculated by using the proposed CoM Jacobian. Finally, computer simulations are performed by utilizing RecurDyn and MATLAB softwares to validate the proposed preview control formulation for the nonlinear walking patterns generation of a Bioloid humanoid robot.

In this paper, a new method for the dynamic analysis of a closed-loop flexible kinematic mechanical system is presented. The kinematic and force models are developed using absolute reference, joint relative, and elastic coordinates as well as joint reaction forces. This recursive formulation leads to a system of loosely coupled equations of motion. In a closed-loop kinematic chain, cuts are made at selected auxiliary joints in order to form spanning tree structures. Compatibility conditions and reaction force relationships at the auxiliary joints are adjoined to the equations of open-loop mechanical systems in order to form closed-loop dynamic equations. Using the sparse matrix structure of these equations and the fact that the joint reaction forces associated with elastic degrees of freedom do not represent independent variables, a method for decoupling the joint and elastic accelerations is developed. Unlike existing recursive formulations, this method does not require inverse or factorization of large non-linear matrices. It leads to small systems of equations whose dimensions are independent of the number of elastic degrees of freedom. The application of dynamic decoupling method in dynamic analysis of closed-loop deformable multibody systems is also discussed in this paper. The use of the numerical algorithm developed in this investigation is illustrated by a closed-loop flexible four-bar mechanism.

In this paper, a non-linear recursive formulation is developed for kinematic and dynamic analysis of open-loop mechanical systems. The non-linear equations of motion are developed for deformable links that undergo large translational and rotational displacements. These equations are formulated in terms of a set of time invariant scalars and matrices that depend on the spatial co-ordinates as well as the assumed displacement field, and these time invariant quantities represent the dynamic coupling between the rigid-body modes and elastic deformations. A new recursive formulation is presented for solving equations of motion for open-loop chains consisting of interconnected rigid and deformable open-loop mechanical systems. This formulation is expressed by the recursive relationships and the generalized non-linear equations for deformable mechanical systems to obtain a large system of loosely coupled equations of motion. The main processor program consists of three main modules: constraint module, mass module and force module. The constraint module is used to numerically evaluate the relationship between the absolute and joint accelerations. The mass module is used to numerically evaluate the system mass matrix as well as the non-linear Coriolis and centrifugal forces associated with the absolute, joint and elastic co-ordinates. Simultaneously, the force module is used to numerically evaluate the generalized external and elastic forces associated with the absolute, joint and elastic co-ordinates. Computational efficiency is achieved by taking advantage of the structure of the resulting system of loosely coupled equations. The solution techniques used in this investigation yield a much smaller operations count and can more efficiently implement in any computer. The algorithms and solutions presented in this paper are illustrated by using an industrial robotic manipulator system. The numerical results using this formulation are also presented and discussed in this paper. Copyright © 2006 John Wiley & Sons, Ltd.

The recursive projection schemes used in most existing recursive methods for solid deformable structure dynamic problems lead to dense coefficient matrices in the acceleration equations and consequently there is a strong dynamic coupling between the joint and elastic coordinates. When the number of elastic degrees of freedom increases, the size of the coefficient matrix in the acceleration equations becomes large and consequently the use of these recursive methods for solving for the joint and elastic accelerations becomes less efficient. This paper discusses the problems associated with the recursive projection schemes used in the existing recursive methods, and it is shown that decoupling the joint and elastic accelerations using the nonlinear recursive method requires the factorization of nonlinear matrices whose dimensions are independent of the number of elastic degrees of freedom of the open-loop and closed-loop system. An amalgamated formulation that can be used to decouple the elastic and joint accelerations is then proposed. The use of the nonlinear recursive method developed in this paper is demonstrated using an open-loop free-falling deformable double pendulum system and a closed-loop four-bar mechanism. Copyright © 2006 John Wiley & Sons, Ltd.