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This paper presents a new approach to calculate the direct and inverse differential kinematics for serial manipulators. The approach is an extension of the Davies method for open kinematic chains based on a virtual kinematic chain concept introduced in this paper. It is a systematic method that unifies the kinematics of serial manipulators considering the type of kinematics and the coordinate system of the operational space and constitutes an alternative way to solve the differential kinematics for manipulators. The usefulness of the method is illustrated by applying it to an industrial robot

A problem still unsolved in kinematics is the enumeration of a complete list of kinematic chains and mechanisms without isomorphisms and without degenerate chains that operate in any screw system. In this paper, a method for the enumeration of kinematic chains without isomorphisms and degenerate chains for all screw systems and a new method of enumeration of kinematic chain inversions (i.e. mechanisms) based on group theory techniques are presented. New concepts of the group theory are introduced and a new method of enumeration of inversions is presented. Kinematic inversions are related to the symmetries of the chain which can be identified analysing the corresponding graph. The symmetry of a graph can be identified for the group of automorphisms of the graph and its orbits provides sets of vertices (links) that are in the same equivalence classes, i.e. they have the same properties of symmetry. The main definitions of group theory and examples of application of the new method of enumeration of inversions are presented. New results are obtained and divided in two classes: original results in non-planar screw systems (λ = 3) and results in agreement with a previously published list for planar kinematic chains and planar mechanisms (inversions). Two tables (1 and 3) are provided, which are up-to-date lists of kinematic chains and mechanisms for several screw systems.

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Foliar spray of treatments in the control of downy mildew and bulb rot in onionA field experiment was carried out to evaluate the effect of foliar sprays with the following treatments on the downy mildew (Peronospora destructor) and bulb rot (Burkholderia cepacia) in onions: non-treated control, fungicide chlorotalonil/metalaxyl + chlorotalonil, potassium phosphite, foliar fertilizer (03-00-16, N-P-K), bordeaux mixture, bordeaux mixture/potassium phosphite, acibenzolar-S-methyl weekly applied; extract of alga Ulva fasciata and ulvan sprayed every 7, 14 and 21 days. Only the weekly spraying of fungicides and fertilizer (03-00-16, 400 mL/100 L) significantly reduced the mildew severity by 60 and 23%, respectively, but did not increase the bulb yield. The foliar application of potassium rich fertilizers resulted in a higher incidence of rotten bulbs after 5 months in storage. Soluble sugar content and rot incidence of onion bulbs were significantly correlated (-0,629, p ≤ 0,05).