A network approach to mechanisms and machines: some lessons learned

This is essentially a review paper describing progress made in treating mechanisms and machines as networks. Some of the terminology that is helpful to this approach is explained. Relevant elements of graph theory are mentioned. The original aim was to find a robust procedure for finding the instantaneous relative motion of all pairs of bodies within a kinematic chain. The manner in which this was achieved produced several other results that have found unanticipated applications. These are mentioned and publications are cited. Lessons have been learned and these are discussed in Section 11

Dual coupling networks

Using dual graphs and dual couplings, it is shown how the dual of a coupling network can be found. The actions that can exist within an overconstrained coupling network are shown to be geometrically identical to the motions that can occur within the dual of that coupling network. Most useful coupling networks, such as mechanisms within machinery, are both overconstrained and underconstrained. Motions of machine parts attributable to underconstraint can be seen thereby making the motions easy to imagine from a drawing. Conversely, internal actions attributable to overconstraint cannot be seen and so are difficult to imagine. Such actions could result in fatigue failure. Thus one possible benefit of creating the dual of a coupling network is that internal actions hidden within it become recognisable motions of bodies in its dual. This article could lead to a better awareness of overconstraint and its dangers

Simple examples of dual coupling networks

Most mechanisms are both underconstrained and overconstrained. The motions attributable to underconstraint can be seen so that they are easily imagined from a drawing whereas actions attributable to overconstraint cannot. Dual coupling networks have the property that the action and motion systems of one are transposed in the other. So, by finding the dual of a mechanism, actions attributable to overconstraint become motions in its dual that can be imagined. Earlier work cited explains the methodology and validates the theory mathematically: this paper provides some simple examples

Planar revolute-coupled kinematic chains in critical configurations and their duals

The motivation for studies of dual coupling networks is explained and a definition is suggested for duality. Dual couplings are defined and several couplings dual with the revolute coupling are described. Six linkages, instantaneously in a critical configuration, provide examples. The consequences of these critical configurations are explored for both the linkages and the coupling networks that are dual with them

Partial cancellation of shaking force harmonics by cam modification

An optimization procedure for minimizing the shaking force harmonics of machinery is described. Because of constraints imposed by the specification, optimization is unlikely to make any significant reduction in the fundamental, machine frequency, term of the shaking force. That term, normally the largest, must be substantially reduced by other means for the procedure described here to be cost effective. Earlier work describing methods of reducing the fundamental term are cited. An extrusion press machine incorporating two planar mechanisms, one crank driven and one cam driven, provides an example. Two designs of the cam-driven mechanism, referred to here as cams 1 and 2, are in use in installed extrusion press machines. Harmonic analysis of the shaking force as a function of time shows that cam 2 produces smaller amplitudes of shaking force harmonics. The ten variables used in the optimization process are the amplitudes and angles of the first five terms of a trigonometric series defining the acceleration of a reciprocating mass driven by a hypothetical third cam, cam 3, which is similar to cam 2 but stripped of all harmonics of order higher than the fifth. The objective function is the sum of the amplitudes of the horizontal components of the second to fifth shaking force harmonics on the machine as a consequence of accelerations of the moving parts of both mechanisms. Several equality and inequality constraints must be met. For the extrusion press machine the result is a reduction in the amplitudes that would be created if cam 3 were to be used by approximately 10, 75, 65 and 100 per cent respectively. The improvement over cam 1 is greater. The procedure is particularly suited as a retrofit measure where the number of installed machines is large in relation to the future rate of production of new machines: a cam that has been removed from one machine can be re-cut for use on another machine

Bs → D*s Form Factors for the full q² range from lattice QCD

We compute the Standard Model semileptonic vector and axial-vector form factors for B s → D ∗ s decay across the full q 2 range using lattice QCD. We use the highly improved staggered quark (HISQ) action for all valence quarks, enabling us to normalize weak currents nonperturbatively. Working on second-generation MILC ensembles of gluon field configurations which include u , d , s , and c HISQ sea quarks and HISQ heavy quarks with masses from that of the c mass up to that of the b on the ensemble with the smallest lattice spacing, allows us to map out the heavy quark mass dependence of the form factors, and to constrain the associated discretization effects. We can then determine the physical form factors at the b mass. We use these to construct the differential and total rates for Γ ( B 0 s → D * − s ℓ + ν ℓ ) and find Γ ℓ = e / | η EW V c b | 2 = 2.07 ( 17 ) latt ( 2 ) EM × 10 13     s − 1 , Γ ℓ = μ / | η EW V c b | 2 = 2.06 ( 16 ) latt ( 2 ) EM × 10 13     s − 1 , and Γ ℓ = τ / | η EW V c b | 2 = 5.14 ( 37 ) latt ( 5 ) EM × 10 12     s − 1 , where η EW contains the short-distance electroweak correction to G F , the first uncertainty is from our lattice calculation, and the second allows for long-distance QED effects. The ratio R ( D * − s ) ≡ Γ ℓ = τ / Γ ℓ = μ = 0.2490 ( 60 ) latt ( 35 ) EM . We also obtain a value for the ratio of decay rates Γ ℓ = μ ( B s → D s ) / Γ ℓ = μ ( B s → D ∗ s ) = 0.443 ( 40 ) latt ( 4 ) EM , which agrees well with recent LHCb results. We can determine V c b by combining our lattice results across the full kinematic range of the decay with experimental results from LHCb and obtain | V c b | = 42.2 ( 1.5 ) latt ( 1.7 ) exp ( 0.4 ) EM × 10 − 3 . A comparison of our lattice results for the shape of the differential decay rate to the binned, normalized differential decay rate from LHCb shows good agreement. We also test the impact of new physics couplings on angular observables and ratios which are sensitive to lepton flavor universality violation

R(J/ψ) and B−c → J/ ψℓ−¯νl lepton flavor universality violating observables from lattice QCD

We use our lattice QCD computation of the Bc→J/ψ form factors to determine the differential decay rate for the semitauonic decay channel and construct the ratio of branching fractions R(J/ψ)=B(B−c→J/ψτ−ντ)/B(B−c→J/ψμ−νμ). We find R(J/ψ)=\rjpsi and give an error budget. We also extend the relevant angular observables, which were recently suggested for the study of lepton flavor universality violating effects in B→D∗ℓν, to Bc→J/ψℓν and make predictions for their values under different new physics scenarios

Advances in the proposed electromagnetic zero-point field theory of inertia

A NASA-funded research effort has been underway at the Lockheed Martin Advanced Technology Center in Palo Alto and at California State University in Long Beach to develop and test a recently published theory that Newton's equation of motion can be derived from Maxwell's equations of electrodynamics as applied to the zero-point field (ZPF) of the quantum vacuum. In this ZPF-inertia theory, mass is postulated to be not an intrinsic property of matter but rather a kind of electromagnetic drag force that proves to be acceleration dependent by virtue of the spectral characteristics of the ZPF. The theory proposes that interactions between the ZPF and matter take place at the level of quarks and electrons, hence would account for the mass of a composite neutral particle such as the neutron. An effort to generalize the exploratory study of Haisch, Rueda and Puthoff (1994) into a proper relativistic formulation has been successful. Moreover the principle of equivalence implies that in this view gravitation would also be electromagnetic in origin along the lines proposed by Sakharov (1968). With regard to exotic propulsion we can definitively rule out one speculatively hypothesized mechanism: matter possessing negative inertial mass, a concept originated by Bondi (1957) is shown to be logically impossible. On the other hand, the linked ZPF-inertia and ZPF-gravity concepts open the conceptual possibility of manipulation of inertia and gravitation, since both are postulated to be electromagnetic phenomena. It is hoped that this will someday translate into actual technological potential. A key question is whether the proposed ZPF-matter interactions generating the phenomenon of mass might involve one or more resonances. This is presently under investigation.Comment: Revised version of invited presentation at 34th AIAA/ASME/SAE/ASEE Joint Propulsion Conference, July 13-15, 1998, Cleveland, OH, 10 pages, no figure

Measuring Selection when Parents and Offspring Interact

Non-social and social selection gradients are key evolutionary parameters in systems where individuals interact. They are most easily obtained by regressing an individual's fitness on the trait values of the individual and its social partner. In the context of parental care it is more common to regress the trait value of the parents (i.e. the social partner) on a ‘mixed’ fitness measure that is a function of the parent's and offspring's fitness (for example, the number of recruits, which equals parental fecundity multiplied by offspring survival). For such an approach to yield correct estimates of net-selection, the trait must be sex-limited and not affect the parents’ own survival. When a trait is not sex-limited, the non-social selection should be weighted by one (because all individuals express the trait) and social selection should be weighted by a half (because the relatedness between parents and the offspring they care for is a half, usually). The ‘mixed’ fitness approach does not give estimates of both components of selection and so they cannot be weighted appropriately. We show that mixed fitness components are frequently used in place of direct fitness measures in the literature (37% of fecundity selection estimates use a mixed fitness approach), but that the frequency is much higher in some taxa, such as birds and mammals. We suggest alternative methods that could be used to estimate both social and non-social selection gradients, while at the same time assessing the importance of unmeasured traits

Lines Missing Every Random Point

We prove that there is, in every direction in Euclidean space, a line that misses every computably random point. We also prove that there exist, in every direction in Euclidean space, arbitrarily long line segments missing every double exponential time random point.Comment: Added a section: "Betting in Doubly Exponential Time.