Motion For Rigid Multibody Systems Research Articles

A comparative study of the principal methods for the analytical formulation and the numerical solution of the equations of motion of rigid multibody systems

The goal of this investigation is to perform a comparative analysis of the principal methodologies employed for the analytical formulation and the numerical solution of the equations of motion of rigid multibody mechanical systems. In particular, three formulation approaches are considered in this work for the analytical formulation of the equations of motion. The multibody formulation strategies discussed in this paper are the Reference Point Coordinate Formulation with Euler Angles (RPCF-EA), the Reference Point Coordinate Formulation with Euler Parameters (RPCF-EP), and the Natural Absolute Coordinate Formulation (NACF). Moreover, five computational algorithms are considered in this investigation for the development of effective and efficient solution procedures suitable for the numerical solution of the equations of motion. The multibody computational algorithms discussed in this paper are the Augmented Formulation (AF), the Embedding Technique (ET), the Amalgamated Formulation (AMF), the Projection Method (PM), and the Udwadia-Kalaba Equations (UKE). The multibody formulation approaches and solution procedures analyzed in this work are compared in terms of generality, versatility, ease of implementation, accuracy, effectiveness, and efficiency. In order to perform a general comparative study, four benchmark multibody systems are considered as numerical examples. The comparative study carried out in this paper demonstrates that all the methodologies considered can handle general multibody problems, are computationally effective and efficient, and lead to consistent numerical solutions.

A natural absolute coordinate formulation for the kinematic and dynamic analysis of rigid multibody systems

The purpose of this paper was to present the key features of a novel coordinate formulation for the analytical description of the motion of rigid multibody systems, namely the natural absolute coordinate formulation (NACF). As it is shown in this work, the kinematic and dynamic analysis of rigid multibody systems can be significantly enhanced employing the NACF. In particular, this formulation combines the main advantages of the natural coordinate formulation (NCF), such as the remarkable property of leading to a constant mass matrix and to zero centrifugal and Coriolis generalized inertia forces, with the generality and the effectiveness of the reference point coordinate formulation (RPCF), which is essentially represented by the possibility to develop and assemble the equations of motion of a multibody system together with the algebraic equations which model the joint constraints in a systematic manner. Moreover, a new computational method hereinafter referred to as the robust generalized coordinate partitioning algorithm is also introduced in this work. The robust generalized coordinate partitioning algorithm can be successfully utilized to numerically solve the index-one form of the multibody system equations of motion formulated by using the proposed NACF as well as the well-known RPCF. In particular, the computational procedure presented in this paper owes its robustness to the combination of the main ideas of the well-established generalized coordinate partitioning method, which is commonly employed to cope with the drift phenomenon of the constraint equations at the position and velocity levels when an index-one formulation of the equations of motion is considered, with the more general and advanced constraint enforcement technique at the acceleration level represented by the fundamental equations of constrained motion. In fact, the fundamental equations of constrained motion represent an effective and efficient method able to calculate analytically the generalized constraint forces relative to a multibody system subjected to a general set of redundant holonomic and/or nonholonomic constraint equations by using the Gauss principle of least constraint, thus avoiding the definition of the Lagrange multipliers. The fundamental equations of constrained motion are remarkably effective when used for modeling the dynamic behavior of rigid multibody systems mathematically represented employing the NACF, as it is shown in this paper. Four simple benchmark multibody systems are also examined in order to exemplify the application of the principal concepts developed in the paper.

Energy Based Indexes for Manipulator Dynamics Improvement

Several indexes for evaluation of nonlinear effects during the motion of rigid multi-body systems are proposed in this paper. All of them are based on the kinetic energy and arise from an analysis of equations of motion expressed in terms of inertial quasi-velocities (IQV). Such equations are first-order and have a diagonal mass matrix of the system. The IQV depend on configuration of the system and take into consideration also its geometrical and inertial parameters. The indexes enable to detect deformation of joint velocity as a consequence of manipulator motion, the kinetic energy resulting from dynamical couplings and the energy transferred by each link individually. Because calculation of these indexes allow to determine influence of couplings on behavior of the manipulator then they can be used in the design phase for analysis and reduction of nonlinear effects in any motion. Simulation and experimental results demonstrate that the proposed indexes are significant for evaluation of nonlinear effects and kinetic energy reduction during the manipulator motion.

Adapting the Principle of Integrated Navigation Systems to Measuring the Motion of Rigid Multibody Systems

During the last years integrated navigation systems based on gyros,accelerometers, and satellite navigation receivers became powerful,favourably priced devices for the guidance of aircraft and ships.Comparable equipment using especially wheel sensors exists for cars. Thekernel of such systems is a Kalman filter estimating the relevantvehicle motion. The filter design in turn requires a kinematical modelto settle on the motion components considered and to describe themechanical meaning of the measurements employed. Up to now, usual modelsrepresent a single rigid body with two, three or six degrees of freedom.

On configurations of symbolic equations of motion for rigid multibody systems

An algorithmic procedure for generating symbolic equations of motion for rigid multibody systems based on a Matrix-Vector approach is presented in this paper. The ease of computation and power inherent in this approach are demonstrated through a series of illustrative examples. Various techniques such as simultaneous generation of second order differential equations of motion and conversion to first order differential equations of motion in Hamiltonian variables, generalized coordinates transformation, order reduction using holonomic and nonholonomic constraint equations and block construction of equations of motion for the compound system from the equations of motion of the sub-systems are described.