Symmetric and Asymmetric Multiple Impulsive Constraints Without Friction and Their Characterization

We present two meaningful and effective non-ideal constitutive characterizations for a multiple impulsive constraints $${\mathcal {S}}$$ S comprising a finite number of non-ideal frictionless constraints of codimension 1, described in the geometric setup given by the space–time bundle $${\mathcal {M}}$$ M of a mechanical system in contact/impact with $${\mathcal {S}}$$ S . Thanks to the geometric structures associated to the elements of $${\mathcal {S}}$$ S , we introduce a symmetric characterization, that does not distinguish the elements forming $${\mathcal {S}}$$ S as regards mechanical behavior, and an asymmetric one that makes this distinction. Both the characterizations provide a generalization of the characterization of ideal multiple constraints presented in Pasquero (Q Appl Math 76(3):547–576, 2018). The iterative nature of these characterizations allows the introduction of two algorithms determining the right velocity of the system in case of single or multiple contact/impact with symmetric or asymmetric constraints $${\mathcal {S}}$$ S , once the elements forming $${\mathcal {S}}$$ S and the left velocity of the system are known. We show the effectiveness of the two possible choices with explicit implementations of these algorithms in two significant examples: a simplified Newton’s cradle system for the symmetric characterization and a disk in multiple contact/impact with two walls of a corner for the asymmetric one.

Considering Link Flexibility in the Dynamic Synthesis of Closed-Loop Mechanisms: A General Approach

This paper has focused on the dynamic analysis of mechanisms with closed-loop configuration while considering the flexibility of links. In order to present a general formulation for such a closed-loop mechanism, it is allowed to have any arbitrary number of flexible links in its chain-like structure. The truncated assumed modal expansion technique has been used here to model link flexibility. Moreover, due to the closed nature of the mentioned mechanism, which imposes finite holonomic constraints on the system, the appearance of Lagrange multipliers in the dynamic motion equations obtained by Lagrangian formulation is unavoidable. So, the Gibbs-Appell (G-A) formulation has been applied to get rid of these Lagrange multipliers and to ease the extraction of governing motion equations. In addition to the finite constraints, the impulsive constraints, which originate from the collision of system joints with the ground, have also been formulated here using the Newton's kinematic impact law. Finally, to stress the generality of the proposed formulation in deriving and solving the motion equations of complex closed-loop mechanisms in both the impact and non-impact conditions, the computer simulation results for a mechanism with four flexible links and closed-loop configuration have been presented.

An Eigenvalue Problem for the Analysis of Variable Topology Mechanical Systems

Mechanical systems with time-varying topology appear frequently in natural or human-made artificial systems. The nature of topology transitions is a key characteristic in the functioning of such systems. In this paper, we discuss a concept that can offer possibilities to gain insight and analyze topology transitions. This approach relies on the use of impulsive constraints and a formulation that makes it possible to decouple the dynamics at topology change. A key point is an eigenvalue problem that characterizes several aspects of energy and momentum transfer at the discontinuous topology transition.

Dynamics of Non-Ideal Topology Transitions in Multibody Mechanical Systems

Mechanical systems with time-varying topology appear frequently in various applications. In this paper, topology changes that can be modeled by means of bilateral impulsive constraints are analyzed. We present a concept to project kinematic and kinetic quantities to two mutually orthogonal subspaces of the tangent space of the mechanical system. This can be used to obtain decoupled formulations of the kinetic energy and the dynamic equations at topology transition. It will be shown that the configuration of the multibody system at topology change significantly influences the projection of non-ideal forces to both subspaces. Experimental analysis, using a dual-pantograph robotic prototype interacting with a stiff environment, is presented to illustrate the material.

The Analysis of Constrained Impulsive Motion

Impulsive problems for mechanical systems subject to kinematic constraints are discussed in this paper. In addition to the applied impulses, there may exist suddenly changed constraints, or termed impulsive constraints. To describe the states of the system during the impulsive motion, three different phases, i.e., prior motion, virtual motion, and posterior motion, are defined which are subject to different sets of constraints, and thus have different degrees-of-freedom. A fundamental principle, i.e., the principle of velocity variation, for the constrained impulsive motion is enunciated as a foundation to derive the privileged impulse-momentum equations. It is shown that for a system with no applied impulse, a conservation law can be stated as the conservation of the virtual-privileged momenta. The proposed methodology provides a systematic scheme to deal with various types of impulsive constraints, which is illustrated in the paper by solving the constrained impulsive problems for the motion of a sleigh.

Modeling and Simulation of Dynamic Mass Capture by Robot Manipulators Considering Structural Flexiblity

In this paper we investigate the dynamics of the process when a robot intercepts and captures a moving object. This operation is called dynamic mass capture. The effects of structural flexibility of the robot is taken into consideration. In terms of time the analysis is divided into three phases: before interception (finite motion), at the vicinity of interception and capture (impulsive motion), and after interception (finite motion). Special attention is paid to the modeling of the second phase when the robot intercepts and captures a target and it becomes part of the end effector, thus, the system’s degrees of freedom and topology suddenly change. To describe this event, an alternative approach is proposed. This is based on the use of a class of impulsive constraints, the so-called inert constraints. Jourdain’s principle is employed to derive the dynamic equations for both finite and impulsive motions. Based on the proposed approach, simulation results are presented for a flexible slewing link capturing a moving target. These results are compared with the observations of an experiment. Good agreement is found between the experimental and simulation results, which suggests that the analysis presented in this paper can be used with confidence in investigations of robots intercepting and capturing moving objects.

Analytical Foundations for Modeling Interactions in Dynamic Systems Based on Impulsive Constraints

In this paper we outline the analytical foundations of an approach for modeling interactions in dynamic systems. The method is based on impulsive constraints which can be employed to represent time-varying interaction of dynamic subsystems, and the transition between different phases of motion. Besides impulsive constraints, the analysis is based on Jourdain’s principle, and a kinematic representation of constrained mechanical systems which is related to this principle. Both finite and impulsive constraints are considered in a general manner, assuming that those can be nonlinear in velocities. It will be shown that Jourdain’s principle can create a simple and physically clear basis for such constrained motion problems. A classification of motions constrained by finite or impulsive constraints is discussed. An impulse-momentum level form of Jourdain’s principle is presented to handle impulsive constraints. An example of two robotic arms in cooperation is employed to illustrate the material presented.