Natural Orthogonal Complement Method Research Articles

Closed-form dynamic modeling and performance analysis of an over-constrained 2PUR-PSR parallel manipulator with parasitic motions

This paper presents an systematic dynamic modeling and performance analysis method of an over-constrained 2PUR-PSR parallel manipulator with parasitic motions, where P, U, S, and R represent the prismatic joint, universal joint, spherical joint, and revolute joint, respectively. The process of the deduction of the over-constrained forces/moment is given. The Newton–Euler approach and natural orthogonal complement method are adopted to establish two types of dynamic models with and without constrained forces/moments with the consideration of the over-constrained forces/moments. The dynamic manipulability ellipsoid, which measures the uniformity of changing the position and orientation of the manipulator’s moving platform, is adopted to evaluate the dynamic performance of the parallel manipulator. To show the feasibility of the proposed method, numerical simulations are conducted to investigate the dynamic models and performance of the 2PUR-PSR manipulator. The actuation forces, constrained forces/moments, and the compatible deformation are calculated. Distribution of the DME index is also obtained. The proposed modeling approach provides a fundamental basis for the structural optimization and control scheme design of the over-constrained parallel manipulator.

Forward dynamic analysis of parallel robots using modified decoupled natural orthogonal complement method

This paper aims at the forward dynamic analysis of parallel robots by adding an effective modification on the Decoupled Natural Orthogonal Complement (DeNOC) method incorporating Virtual Spring Method (VSM). Forward dynamic analysis of parallel manipulators have been studied by many researches during the last decades, however, due to the complexity of closed-loop structures, it is still an attractive research subject in robotics. Developing VSM in energy based dynamic methods i.e., Lagrange formulation, has been demonstrated in literature before. In the current work, first, the VSM is briefly reviewed and its liaison with the Augmented Lagrange Method (ALM) is discussed. Next, among the Newtonian methods, the DeNOC which is based on the screw theory is elaborated. Then, inspired by the relation between VSM and ALM, the modified DeNOC (MDeNOC) is introduced. For more clarification, a 2DOF-five bar planar mechanism is chosen as case study and the aforementioned dynamic approaches are applied. Finally, the advantages and disadvantages of each method are illustrated. The key advantage of MDeNOC method is the ability of dynamic response and constraint reactions calculations with less preparation effort compared to DeNOC, while its accuracy is similar to Lagrange-VSM.

Inverse dynamics of a 3-prismatic—revolute—revolute planar parallel manipulator using natural orthogonal complement

The performance of robotic systems with parallel kinematics can be evaluated by their kinematic, static, and dynamic properties. These properties are directly used in model-based controllers which potentially offer higher accuracy for robotic systems. Inverse dynamic solution is an essential part of these controllers. In the present work, the inverse dynamics model of a 3-PRR (prismatic—revolute—revolute) planar parallel manipulator based on the natural orthogonal complement (NOC) method is developed. To drive the NOC for the 3-PRR closed-loop systems, the explicit expressions of the loop constraints equations and the associated Jacobian matrices are first obtained. Next the NOC matrix, which is a velocity transformation matrix relating the Cartesian angular/translational velocities of various bodies to the motor joint rates, is calculated. Finally results of the NOC method are compared with simulation of a 3-PRR planar parallel manipulator using two commercial softwares: SimMechanics toolbox of Matlab and COSMOSMotion of SolidWorks. In order to verify the theoretical results, two different configurations for the robot are considered: a horizontal and a vertical. Results of the NOC method as well as the two simulations are compared for the two robot configurations.

Dynamics and Cooperative Object Manipulation Control of Suspended Mobile Manipulators

Dynamics and control of mobile manipulators is obviously a more challenging problem compared to fixed-base robots. Including a suspension system for these mobile platforms increases their maneuverability, but considerably adds to their complexity. In this paper, a suspended wheeled mobile platform with two 6-DOF Puma-type manipulators is used to manipulate an object along a given path. To apply a model-based control algorithm, it is required to have an explicit dynamics model for such highly nonlinear system. This model should be as concise as possible to include fewer mathematical calculations for online computations. Therefore in this paper, a detailed set of dynamics equations for a multiple arm wheeled mobile platform equipped with an effective suspension system is presented. The method is based on the concept of Direct Path Method (DPM), which is extended here for such challenging type of robots. The obtained dynamics model is then verified with a dynamical analysis study using software ADAMS. Then, Natural Orthogonal Complement Method is used to include the non-holonomic constraint of the wheeled platform in a more concise dynamics model. Next, an impedance control law is applied for cooperative manipulation of an object by the two manipulators. The obtained results for a suspended wheeled platform equipped with two 6-DOF Puma-type manipulators reveal a successful performance for moving an object along a mixed circular-straight path, even in the presence of unexpected disturbing forces, system/end-effector flexibility and impacts due to contact with an obstacle.

A novel formulation of the dynamic balancing of five-bar linkages with applications to link optimization

In this report, we derive design equations and techniques for the dynamic balancing of five-bar linkage, using a novel and simplified approach. Firstly, in order to derive the dynamic equations of the mechanism we have applied the natural orthogonal complement method. Subsequently, an optimization method for the dynamic balancing of the linkage is proposed. The conditions of dynamic balancing of the five-bar linkage are expressed as seven equations and four inequalities, with twelve linkage parameters. The dynamic balancing of the mechanism is formulated and solved as an optimization problem under equality constraints. The application of the new approach is illustrated through a numerical example.

Tripod Dynamics and Its Inertia Effect

In this paper the tripod dynamics and its inertia effect is studied. The tripod design is becoming popular for the development of parallel kinematic machines (PKMs). The combination of a tripod with a gantry system forms a hybrid machine that offers the advantages from both serial and parallel structures. The tripod dynamics under study includes the mass of the moving platform as well as those of the legs. The natural orthogonal complement method is applied to derive the dynamic equations. The inertia effect of the moving platform and the legs is investigated in terms of two parameters, namely, the ratio of the total leg mass to the mass of the moving platform, and the velocity of the moving platform. The dynamic equations are separated by three terms, inertia, coupling, and gravity. Quantitative studies are carried out by simulation to examine how the two parameters affect the three respective terms. Based on the simulation results, the dynamic equations can be simplified by retaining the dominant terms while neglecting less significant ones. The simplified dynamic equations provide an efficient model for design and control of tripods.

Kinematics, dynamics and control of a hybrid robot Wheeleg

In this paper, we propose a mathematical model for the kinematics of a hybrid robot, called Wheeleg. The wheeled-legged robot has two pneumatically actuated front legs, each with three degrees of freedom, and two rear wheels independently actuated. Based on the proposed model, the dynamics equations of the manipulator are developed using the natural orthogonal complement method. Equations are implemented in an algorithm used to study the kinematics and the dynamics of the mobile robot. Simulations are provided to demonstrate the method developed. Successively, a brief description is given of the control architecture designed and implemented. In conclusion, some experimental tests of the motion on the horizontal plane are reported.

Inverse dynamics of hexapods using the natural orthogonal complement method

The hexapods under study are parallel mechanisms made of fixed-length legs, as opposed to conventional hexapods with extensible legs. The former are becoming popular in developing machine tools for high-speed machining applications. In this paper, the inverse dynamics of hexapods with fixed-length legs is analyzed using the natural orthogonal complement method. This analysis includes the mass of the moving platform as well as those of the legs. The leg masses become important for high-speed applications. In this development, the Newton-Euler formulation is used to model the dynamics of each individual body, including the moving platform and the legs. This is followed by assembling the individual dynamics equations to form the global dynamics equations. Based on the complete kinematics model developed in the paper, an explicit expression is derived for the natural orthogonal complement that effectively eliminates the constraint forces in the global dynamics equations. This leads to the inverse dynamics equations of the hexapods that can be used to compute required actuator forces for given motions. Simulations are provided to demonstrate the developed method.

Inverse dynamics of hexapods using the natural orthogonal complement method : Fengfeng Xi, Rosario Sinatra, v21, n2, 2002, pp73–82

For decades, the arithmetic average (AA or Ra) and root sum of squares (RSS or Rq) have been the two major surface roughness measures to define a broad range of surfaces for a mechanical product. A number of drawbacks have been identified in recent years with the above measures. To map more scientifically and closely the surface roughness to the product functions and performances, ISO 13565 has defined a different set of measures, including Rk, Rpk, Rvk, Mr1, and Mr2. This has not only made process planning different and much more difficult, but also made modeling of the relationship between these roughness measures and the machining parameters a multiple-input and multiple-output problem. While some companies are trying the traditional trial-and-error method to implement the ISO 13565 standard, this study applies artificial neural networks to develop an empirical model for the honing process of engine cylinder liners in order to help reduce emissions, improve oil efficiency, and prolong engine life. Threefold cross-validation is applied to develop the models. Hypothesis testing and the prediction error statistics are employed to select the best model. Data from industrial experiments based on fractional factorial design will illustrate th goodness of the modeling approach and the models.

Developing algorithms for efficient simulation of flexible space manipulator operations

A brief description is given of the European Robot Arm (ERA), and its intended application to assembly, maintenance and servicing of the Russian segment of the International Space Station Alpha. The need for manipulator simulation is recalled, and ERA simulator development is outlined. System characteristics that must be modelled for incorporation in the dynamics kernel for the simulator are mentioned. A brief review is presented of efficient Order- N 3 and Order- N algorithms for the simulation of manipulator dynamics. Parenthetically the existence of a link between Kane's method, the natural orthogonal complement method, and Jourdain's principle is indicated. An algorithm of the Order- N type has then been developed and implemented in the ERA simulation facility. Some numerical results are presented, displaying accuracy as well as computational efficiency.