Carlo Galletti

Single-loop kinematotropic mechanisms

Abstract The paper concerns the chains in which changes in certain position variables can lead to changes in the permanent finite mobilities of the chains: this property is called “kinematotropy”. We present a systematic approach that allows us to form four basic kinematotropic single-loop chains. Then we show how to modify these chains to obtain various kinematotropic mechanisms. One of the presented chains can have 1 or 2 degree(s) of freedom, depending on its position; the three remaining chains can have 2 or 3 degrees of freedom. The approach we use to derive the chains is based on the theory of displacement groups. Finally, an extension of the method to multiloop chains is discussed.

Parallel robots that change their group of motion

In this work we present several parallel robots with reduced mobility whose platforms can change their subgroups of displacement when the robot is displaced continuously from one set of positions to another one. In some cases, also the number of degrees of freedom of the platform may change, in other cases, only the group of displacement or its invariant properties are modified. By using some results on mobility of single-loop kinematic chains based on the theory of the displacement groups, the way to synthesize these robots is discussed.

Metric Relations and Displacement Groups in Mechanism and Robot Kinematics

This paper presents a systematic theory for metric relations between the invariant properties of displacement groups, and shows this theory application to mechanism kinematics. Displacement groups, their invariant properties and operations are briefly described. Kinematic constraints are then introduced as tools for relating abstract group properties to actual mechanism constraints. Criteria and operating rules to employ metric relations for the generation of a meaningful set of closure equations for kinematic chains are detailed.

A note on modular approaches to planar linkage kinematic analysis

Abstract This paper presents a structure-based method for determining and solving linkage compatibility equations by uncoupling procedures. On the basis of early work by Assur and other authors, the systematic method proposed can be utilized to generate and analyze mechanisms of any complexity and degree of freedom. It is shown that only one kind of link structure (Assurs kinematic chain) is required to implement this method. Applications to computer-aided analysis are also discussed.

Mobility analysis of single-loop kinematic chains: an algorithmic approach based on displacement groups

Abstract This paper presents a systematic approach to computing the mobility properties of single-loop kinematic chains. Such properties are defined by: the connectivity between any two links in a chain, the displacement group of their relative motion and the invariant properties of this group. Explicit rules and procedures for analyzing open and closed chains are fully described. The proposed approach does not require the knowledge of one closure of the links in the chain, nor the values of the pair variables of the chain. Several examples are given.

Multiloop Kinematotropic Mechanisms

Starting from single-loop kinematic chains whose pairs present different connectivities when the chains are displaced in different positions, the paper shows how to assemble multiloop chains with numbers of degrees of freedom that change due to continuous variations in the position variables of the chains. This special mobility property is called kinematotropy. The paper provides a method (based on the displacement group theory) to form chains that allow any desired change in the number of degrees of freedom, with a sudden or gradual increment of this number. Several examples are presented and applications are discussed.Copyright

Particular or general methods in robot kinematics?: Both particular and general

Abstract The possibility to compound the conflicting characteristics of general and particular methods for analyzing robot-arms and one-closed-loop spatial mechanisms is discussed. To this purpose, a structure-based approach is presented from which various widely known methods can be derived. The possibility of better understanding the geometric nature of a kinematic problem is pointed out, and it is shown how to find a solution pattern for closure problems.

A Modular Method for Computational Kinematics

A modular method for symbolic kinematic modelling of multiloop mechanisms is outlined. For a given mechanism, the method identifies automatically a list of modules for which closure equations can be generated and solved hierarchically. Closed-form solutions can be obtained in many cases of practical interest.

Kinematics of robot mechanisms with closed actuating loops

The kinematic properties of multiloop chains for robot appli cations are investigated using a structure-based approach. The basic concepts related to algebraic groups of displace ments and to Assurs groups are used in order to provide systematic foundations for analysis and synthesis procedures. Analysis techniques are described, and several examples of real applications are given.

An explicit independent-coordinate formulation for the equations of motion of flexible multibody systems

Abstract In this paper, we develop an expression for the equations of motion of multibody systems with rigid and flexible bodies performing any kind of motion, with fixed and time-dependent holonomic constraints, forming open and closed loops, and with constant field forces and generic forces acting on the bodies. The proposed equations have been obtained by Lagrange’s approach and are formulated in terms of independent coordinates; influence coefficients, pseudo-velocities and pseudo-accelerations are used to take into account constraints; modal superposition techniques model body deformations; mass properties of flexible bodies are expressed by invariants of inertia. The final expression of the equations is suited for computer solution and is aimed at reducing to a minimum the number of kinematic analyses required to evaluate influence coefficients and their derivatives.