Mechanical models and the mobility of robots and mechanisms

Abstract

Link to this article: http://journals.cambridge.org/abstract_S0263574714000149How to cite this article: Doru Talabă (2015). Mechanical models and the mobility of robots and mechanisms. SUMMARYMobility is a fundamental parameter of mechanisms expressing in a qualitative manner their kinematic and dynamic properties. The mobility formulae presented in literature take into consideration some of the structural entities, such as bodies, joints, constraints, closed loops, and space characteristics; however, the specific mechanical model that has traditionally been at the origin of the mobility criteria themselves is incompletely specified and, even then, only implicitly. In this paper, we propose a classification of the mobility criteria based on the known dynamic models. While all known mobility criteria have been associated with a specific dynamic model, some particular, less used dynamic models (like natural coordinates and multi-particle models) suggested new mobility criteria models. The associated mechanical model for each category of mobility criteria allows a qualitative assessment of the kinematic and dynamic sets of equations to be formulated in later stages of analysis. A simple multi-loop mechanism is taken as an example just to illustrate the mobility calculation and qualitative assessment of the kinematic and dynamic models in each case. Based on the proposed classification of the mobility formulae, an assessment is made with particular regard to their applicability to overconstrained mechanisms.

Another Multibody Dynamics in Natural Coordinates through Automatic Differentiation and High-Index DAE Solving

“…We refer to the above coefficients as Taylor coefficients (TCs). By equating the TCs in (20,21,22) to zero, we solve for the TCs of u, v, λ. This is not obvious from (20,21,22), but proceeds as follows.…”

“…Before integration starts, Daets performs SA by executing the f i 's code, here fcn, through operator overloading to find the DAE index, dof, and the offset vectors. Then the solver executes the same function with FADBAD++'s Taylor series class to build in memory a computational graph, which is evaluated on each integration step to compute TCs for the f i 's; in our example (20,21,22).…”

“…This is useful here, because subsystem ABCD becomes overconstrained if the spine directions of its four revolute joints are treated as independent. With exact alignment it can move but with small random deviations, mathematically it cannot-the issue of "paradoxical mobility", see Talaba [21] for a good discussion.…”

Kinematic topology and constraints of multi-loop linkages

“…An extension to MBSs has been presented in ref. [45] where rigid subgraphs of points are assigned dynamic properties.…”

Parameter Estimation from Motion Tracking Data

“…For each mechanical joint the constraints equation can be formulated [16], the number of them is depending on the degree of freedom of the joint [17]. The sum of the number of constraint equation and the degree of freedom of the joint is equal to the associated space dimension, 3 in the planar case and 6 in spatial case.…”