The “point of isotropy” and other properties of serial and parallel manipulators

Optimization and comparison between two 6-DoF parallel kinematic machines for HIL simulations in wind tunnel

“…In order to normalize all the terms of the jacobian matrix and to consider the isotropy of the machine it's necessary to use a scale factor defined as characteristic length. The study of the isotropy of PKMs depending on their design parameters is a field in which many researchers are involved [5,6].The characteristic length is defined in many ways in literature, in this paper the definition provided by Fassi and Legnani in [7] is used. This parameter allows to define a normalized Jacobian matrix which is used for the formulation of the kinetostatic constraint and is denoted as ‫ܬ[‬ ].…”

Indirect adaptive fuzzy control for industrial robots: A solution for contact applications

“…In addition, unlike the former, they are time-varying and change in magnitude during manipulator operations. The main effect of both of these error sources is causing discrepancies between the real robot ACCEPTED MANUSCRIPT A C C E P T E D M A N U S C R I P T and its kinetostatic and dynamic model from which its characteristics are derived (Legnani, Tosi, Fassi, Giberti, & Cinquemani, 2010) and on which control is based (Dietz et al, 2012).…”

A combinatorial search method for the quasi-static payload capacity of serial modular reconfigurable robots

“…The GA is performed sequentially to solve Eqs. (2) to (4) using MRR forward kinematics found in [3,9,16], thereby accounting for all possible MRR poses. Due to the stochastic nature of GA/NSGA-II solutions, a stability check is performed.…”

“…This was caused by two reasons: first, the transformation matrix terms do not have similar units, and second, the condition number of the twist transformation does not take into account module self-weights, as shown in [14]. Previously, other parameters such as stiffness ellipsoids were also derived assuming external end-effector payloads and do not take into account individual component self-weights [15,16]. Thus, direct evaluations of the deflections and torques are more reliable methods for assessing the stiffness performance of assembled MRR modules.…”