HAL is a multidisciplinary open access archive for the deposit and dissemination of scientific research documents, whether they are published or not. The documents may come from teaching and research institutions in France or abroad, or from public or private research centers. L'archive ouverte pluridisciplinaire HAL, est destinée au dépôt et à la diffusion de documents scientifiques de niveau recherche, publiés ou non, émanant des établissements d'enseignement et de recherche français ou étrangers, des laboratoires publics ou privés.

Cover design by Volkert van der Wijk, based on World of Motion (2001) by Volkert van der Wijk, an action painting on a 4.88 m wide and 1.58 m high canvas created with moving bicycle parts smeared with paint. Copyright c⃝2014 Volkert van der Wijk (www.kineticart.nl) All rights reserved. No part of this book may be reproduced in any form or by any electronic or mechanical means, including information storage and retrieval systems, without written permission from the author, except in the case of a reviewer, who may quote brief passages embodied in critical articles or in a review.

The major disadvantage of existing dynamic balancing principles is that a considerable amount of mass and inertia is added to the system. The objectives of this article are to summarize, to compare, and to evaluate existing complete balancing principles regarding the addition of mass and the addition of inertia and to introduce a normalized indicator to judge the balancing performance regarding the addition of mass and inertia. The balancing principles are obtained from a survey of literature and applied to a double pendulum for comparison, both analytically and numerically. The results show that the duplicate mechanisms principle has the least addition of mass and also a low addition of inertia and is most advantageous for low-mass and low-inertia dynamic balancing if available space is not a limiting factor. Applying countermasses and separate counter-rotations with or without an idler loop both increase the mass and inertia considerably, with idler loop being the better of the two. Using the force-balancing countermasses also as moment-balancing counterinertias leads to significantly less mass addition as compared with the use of separate counter-rotations. For low transmission ratios, also the addition of inertia then is smaller.

No abstract

Dynamic balance is an important feature of high speed mechanisms and robotics that need to minimize vibrations of the base. The main disadvantage of dynamic balancing, however, is that it is accompanied with a considerable increase in mass and inertia. Aiming at low-mass and low-inertia dynamic balancing, in this article the relative importance of the balance parameters of common balancing principles is analyzed and the balancing principles are compared. To do this, the evaluation of a balanced rotatable link is found to be representative for a large group of balanced mechanisms. Therefore, a rotatable link is balanced with duplicate mechanisms (DM), with a countermass (CM) and a separate counter-rotation (SCR), and with a counter-rotary countermass (CRCM). The equations for the total mass and the inertia are derived and compared analytically while the balancing principles are compared numerically. The results show that the DM-balanced link is the best compromise for low mass and low inertia but requires a considerable space. For the CRCM-balanced link and the SCR-balanced link that are more compact, there is a trade-off between mass and inertia for which the CRCM-balanced link is the better of the two.