Static Balancing of SpringLoaded Planar Revolute-Joint Linkages Without

Abstract We present a method to statically balance a general treestructured, planar revolute-joint linkage loaded with linear springs or constant forces without using auxiliary links. The balancing methods currently documented in the literature use extra links; some do not apply when there are spring loads and some are restricted to only two-link serial chains. In our method, we suitably combine any non-zero-free-length load spring with another spring to result in an effective zero-free-length spring load. If a link has a single joint (with the parent link), we give a procedure to attach extra zero-free-length springs to it so that forces and moments are balanced for the link. Another consequence of this attachment is that the constraint force of the joint on the parent link becomes equivalent to a zero-free-length spring load. Hence, conceptually, for the parent link, the joint with its child is removed and replaced with the zero-free-length spring. This feature allows recursive application of this procedure from the end-branches of the tree down to the root, satisfying force and moment balance of all the links in the process. Furthermore, this method can easily be extended to the closed-loop revolute-joint linkages, which is also illustrated in the paper

Antenatal dexamethasone for early preterm birth in low-resource countries

BACKGROUND: The safety and efficacy of antenatal glucocorticoids in women in low-resource countries who are at risk for preterm birth are uncertain. METHODS: We conducted a multicountry, randomized trial involving pregnant women between 26 weeks 0 days and 33 weeks 6 days of gestation who were at risk for preterm birth. The participants were assigned to intramuscular dexamethasone or identical placebo. The primary outcomes were neonatal death alone, stillbirth or neonatal death, and possible maternal bacterial infection; neonatal death alone and stillbirth or neonatal death were evaluated with superiority analyses, and possible maternal bacterial infection was evaluated with a noninferiority analysis with the use of a prespecified margin of 1.25 on the relative scale. RESULTS: A total of 2852 women (and their 3070 fetuses) from 29 secondary- and tertiary-level hospitals across Bangladesh, India, Kenya, Nigeria, and Pakistan underwent randomization. The trial was stopped for benefit at the second interim analysis. Neonatal death occurred in 278 of 1417 infants (19.6%) in the dexamethasone group and in 331 of 1406 infants (23.5%) in the placebo group (relative risk, 0.84; 95% confidence interval [CI], 0.72 to 0.97; P=0.03). Stillbirth or neonatal death occurred in 393 of 1532 fetuses and infants (25.7%) and in 444 of 1519 fetuses and infants (29.2%), respectively (relative risk, 0.88; 95% CI, 0.78 to 0.99; P=0.04); the incidence of possible maternal bacterial infection was 4.8% and 6.3%, respectively (relative risk, 0.76; 95% CI, 0.56 to 1.03). There was no significant between-group difference in the incidence of adverse events. CONCLUSIONS: Among women in low-resource countries who were at risk for early preterm birth, the use of dexamethasone resulted in significantly lower risks of neonatal death alone and stillbirth or neonatal death than the use of placebo, without an increase in the incidence of possible maternal bacterial infection.Fil: Oladapo, Olufemi T.. Organizacion Mundial de la Salud; ArgentinaFil: Vogel, Joshua P.. Organizacion Mundial de la Salud; ArgentinaFil: Piaggio, Gilda. Organizacion Mundial de la Salud; ArgentinaFil: Nguyen, My-Huong. Organizacion Mundial de la Salud; ArgentinaFil: Althabe, Fernando. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Parque Centenario. Centro de Investigaciones en Epidemiología y Salud Pública. Instituto de Efectividad Clínica y Sanitaria. Centro de Investigaciones en Epidemiología y Salud Pública; ArgentinaFil: Metin Gülmezoglu, A.. Organizacion Mundial de la Salud; ArgentinaFil: Bahl, Rajiv. Organizacion Mundial de la Salud; ArgentinaFil: Rao, Suman P.N.. Organizacion Mundial de la Salud; ArgentinaFil: de Costa, Ayesha. Organizacion Mundial de la Salud; ArgentinaFil: Gupta, Shuchita. Organizacion Mundial de la Salud; ArgentinaFil: Shahidullah, Mohammod. No especifíca;Fil: Chowdhury, Saleha B.. No especifíca;Fil: Ara, Gulshan. No especifíca;Fil: Akter, Shaheen. No especifíca;Fil: Akhter, Nasreen. No especifíca;Fil: Dey, Probhat R.. No especifíca;Fil: Abdus Sabur, M.. No especifíca;Fil: Azad, Mohammad T.. No especifíca;Fil: Choudhury, Shahana F.. No especifíca;Fil: Matin, M.A.. No especifíca;Fil: Goudar, Shivaprasad S.. No especifíca;Fil: Dhaded, Sangappa M.. No especifíca;Fil: Metgud, Mrityunjay C.. No especifíca;Fil: Pujar, Yeshita V.. No especifíca;Fil: Somannavar, Manjunath S.. No especifíca;Fil: Vernekar, Sunil S.. No especifíca;Fil: Herekar, Veena R.. No especifíca;Fil: Bidri, Shailaja R.. No especifíca;Fil: Mathapati, Sangamesh S.. No especifíca;Fil: Patil, Preeti G.. No especifíca;Fil: Patil, Mallanagouda M.. No especifíca;Fil: Gudadinni, Muttappa R.. No especifíca;Fil: Bijapure, Hidaytullah R.. No especifíca;Fil: Mallapur, Ashalata A.. No especifíca;Fil: Katageri, Geetanjali M.. No especifíca;Fil: Chikkamath, Sumangala B.. No especifíca;Fil: Yelamali, Bhuvaneshwari C.. No especifíca;Fil: Pol, Ramesh R.. No especifíca;Fil: Misra, Sujata S.. No especifíca;Fil: Das, Leena. No especifíca

A Global Constraint On Relative Rotation To Avoid Lumped Compliant Mechanisms In Topology Optimization

Some of the well known formulations for topology optimization of compliant mechanisms could lead to lumped compliant mechanisms. In lumped compliance, most of the elastic deformation in a mechanism occurs at few points, while rest of the mechanism remains more or less rigid. Such points are referred to as point-flexures. It has been noted in literature that high relative rotation is associated with point-flexures. In literature we also find a formulation of local constraint on relative rotations to avoid lumped compliance. However it is well known that a global constraint is easier to handle than a local constraint, by a numerical optimization algorithm. The current work presents a way of putting global constraint on relative rotations. This constraint is also simpler to implement since it uses linearized rotation at the center of finite-elements, to compute relative rotations. I show the results obtained by using this constraint oil the following benchmark problems - displacement inverter and gripper

Glenea vellayaniensis Hiremath & Lin 2021, sp. nov.

Glenea vellayaniensis sp. nov. (Figures 1–12) Type material Holotype: ♂, (1) India: Kerala / Vellayani / 8.43333333 N, 76.98416667 E / 5 May 2019, at light / S. R. Hiremath Coll. (2) HOLOTYPE/ Glenea vellayaniensis sp. nov. /des. Hiremath and Lin, 2020 (red label). Paratypes (2 specimens, both with a white locality label as given below, besides a second pink label: ‘ PARATYPE / Glenea vellayaniensis sp. nov. /des. Hiremath & Lin, 2020’): 1♀ with label as follows: India: Kerala / Vellayani; 17. November. 2016/ 8.43333333 N, 76.98416667 E /S. R. Hiremath Coll.; 1♀ with label as follows: India: Kerala / Vellayani; 5. i. 2017 / 8.43333333 N, 76.98416667 E /S. R. Hiremath Coll. Description Male (n = 1) (Figure 1). Body length measured from vertex to elytral apex 6.29 mm; humeral width 1.92 mm. General body colour reddish brown; head, antennomeres I–II, pronotum, elytra and ventral side of body reddish brown; apical half of mandibles black; anteclypeus and antennomeres III–XI yellowish brown; maxillary and labial palpi, legs (except tarsal claws) yellowish brown; tarsal claws reddish brown. Head with frons thickly adpressed with cream yellow hairs; outer margin of upper eye lobes on each side of vertex ornamented with transverse, oblong band of adpressed yellow hairs; area surrounding lower eye lobes, gena, postclypeus thickly adpressed with white hairs. Basal half of mandibles adpressed with thick white hairs. Apical half of labrum adpressed with transverse band of pale white hairs; middle portion of labrum adorned with transversely arranged, seven golden yellow suberect setae, setae at middle smaller than remaining. Head slightly wider than pronotum, randomly covered with punctures subequal in size to those on pronotum, medially impressed with a fine dark brown longitudinal sulcus running from postclypeus to vertex. Labrum thick, protruding, longer than anteclypeus, lying over mandibles; mandibles concealed in frontal view; dorsal surface of labrum with a median transverse ridge, followed by a postmedian shallow excavation; apical margin smooth and truncated. Eyes with lower lobes 2.17 times as long as gena, connected to upper lobes by five rows of ommatidia. Antennal tubercles weakly developed, widely separated, with space between them transversely flat. Antenna with antennomeres I–VII moderately setose beneath with dark brown suberect setae; integument of antennomere I–XI uniformly covered with dark brown and yellowish brown recumbent setae. Antennae surpassing elytral apex near distal end of antennomere VIII, 1.35 times as long as body. Scape thick, cylindrical, slightly narrowed at base, integument uniformly covered with shallow punctures. Ratio of lengths of antennomeres: 1.00: 0.29: 1.35: 1.35: 1.06: 1.00: 0.94: 0.88: 0.88: 0.82: 0.82. Pronotum with pronotal disc faintly covered with yellowish brown recumbent setae, intermixed with uniformly distributed golden yellow erect setae originating from respective punctures; pronotal disc, on each side, ornamented with a broad, longitudinal, sublateral band of thick, adpressed creamy yellow hairs, turning white postmedially, inner margin of this band distinctly concave at its proximal third; lower lateral sides of pronotum, on each side, just above procoxae ornamented with a broad, longitudinal band of thick adpressed white hairs; basal middle of pronotum ornamented with a short, angulate patch of thickly adpressed hairs, white intermixed with yellow; centro-notal area with pubescence of white and yellowish brown disposed into a faint, median, narrow longitudinal band. Pronotum transverse, 1.15 times as wide as long, 0.68 times as long as humeral width; apical margin broader than basal margin; lateral margin on each side slightly swollen at middle and weakly constricted before basal margin. Pronotal disc densely covered with fine punctures; impressed ante-basally with a shallow, transverse groove; pronotal disc just before ante-basal groove, impressed at its middle with a weakly raised, short ridge. Apical margin straight, basal margin weakly sinuate. Scutellum short, tongue-shaped with distinctly arcuate apex; prominently covered with thickly adpressed yellow hairs. Elytra uniformly covered with moderately dense, yellowish grey pubescence; elytral disc uniformly intermixed with suberect golden yellow setae arising from respective punctures; outer margin and apex of elytron fringed with single row of golden yellow suberect setae. Elytral disc, on each side, ornamented with pubescent spots arranged as follows: pre-medially with two spots, medially with one and post-medially with four spots along with a short, sub-lateral pubescent band. First premedian spot located at basal quarter, between humeral prominence and scutellum, made up of thick yellow pubescence, large, broadly bean-shaped with white halo on its borders; second premedian spot located sub-laterally at basal third, small, oval, made up of thick white hairs. Median spot largest, placed between sutural and sub-lateral margins, transversely oval, made up of thick yellow hairs bordered with halo of white hairs; anterior margin angulate at its middle, posterior margin obliquely straight. Post-median spots arranged as follows: first and second spots placed obliquely side by side, just behind middle; first spot located along sutural margin, hemispherical, made up of thick yellow hairs bordered with halo of white hairs, antero-laterally joins median spot along sutural margin; second spot touches sub-lateral margin, circular, made up of thick white hairs; third spot at apical third of elytral disc, largest of post-median spots, made up of thick yellow hairs, bordered with halo of white hairs; second and third spots joined laterally along sub-lateral margin by a short, narrow, longitudinal band of white hairs; fourth spot located on elytral apex, transversely oval, subequal in size to first and second post-median spots, made up of thick yellow hairs, anteriorly bordered with narrow band of white hairs. Elytra elongate, 0.68 times as long as body, 3.30 times as long as pronotum, 2.22 times as long as humeral width; broadest at base, gradually narrowed towards apex. Humeral prominence well developed, obtusely ridged. Sublateral margin impressed with a longitudinal carina, slightly curved at basal fourth, originating from humeral prominence, extending to apical third of elytra. Elytral disc dorsally flat, coarsely punctate up to apical third, punctures becoming finer towards apex; elytral apex truncate with sutural angle dentate and marginal angle stretched into acute spine. Legs with faintly adpressed golden yellow recumbent setae, long and dense on tibiae, interspersed with randomly distributed suberect setae of similar colour. Tarsal claws appendiculate on all legs. Sternites with median portion of pro-, meso- and metasternum uniformly covered with fine, golden yellow recumbent hairs; mesepisternum, mesepimeron and metepisternum thickly adpressed with creamy white hairs; lateral sides of metasternum thickly adpressed with creamy yellow hairs. Abdomen with median longitudinal space uniformly covered with golden yellow recumbent hairs. Ventrites I–IV, laterally on each side, ornamented with a large, thickly adpressed white-haired spot. Sternite VII, laterally on either side with a post-basal spot of similar hairs as previous. Abdomen with sternite VII 0.23 times as long as abdomen, 1.33 times as long as previous segment; disc without a medio-longitudinal sulcus; apex weakly emarginate. Male genitalia (Figures 4–6). Tergite VIII (Figure 4) trapezoidal with apical margin truncated, moderately fringed with light brown elongate setae; lateral margins weakly curved in basal third, fringed with light brown elongate setae from basal third to apex, sparser proximally, denser at distal fourth on inner side; median disc of tergite VIII adorned with randomly distributed light brown, minute, adpressed setae of similar colour. Sternite VIII rectangular, proximal two-thirds with angular reddish brown patch, apex on each side of middle adorned with a transverse patch of medium to elongate, light brown, suberect setae. Spiculum gastrale about 4.43 times as long as spiculum relictum, Y-shaped with median arm slightly longer than lateral arms, distinctly curved at apex; lateral arms obliquely straight, bearing membranous dilation at their distal end. Tegmen (Figure 5 (a– c)) about 1.43 mm long, curved at middle in lateral view (Figure 5 (c)). Basal piece present, reddish brown, distally arcuate, entire surface uniformly covered with minute, suberect spinules. Roof present. Ringed part converging, constricted near widest portion; manubrium hollow, thick in appearance due to internally explanated membrane on each side, in both dorsal and ventral planes; constricted just before basal end; basal end of manubrium abridged by a rectangular membrane, truncated apically (Figure 5 (a)). Lateral lobes (Figure 5 (b)) separated, about 0.25 times as long as total length of tegmen with basal margins transversely ridged; inner margins straight, outer margins oblique, gradually arcuate towards apex; apex rounded. Integument in ventral view red-brown except for a small lighter apical area; basal margin of integument impressed with a transverse row of reddish brown, medium sized, suberect setae; remaining surface randomly covered with similar setae except for a few glabrous spaces near central area; apex concentrated with elongate light brown setae. Median lobe (Figure 6 (a–b)) subequal to length of tegmen, arcuate in lateral view; basal struts originate almost near apical fourth; ventral plate (Figure 6 (b)) dark brown at apical one-fifth, interspersed with a few randomly distributed punctures; apex obtusely pointed, lateral sides asymmetrical, with right side weakly concave near apex. Endophallus (Figures 7–9) in lateral view about 3.90 times as long as median lobe; BPH about 0.28 times as long as endophallus, with membrane transversely plicate; distal end bearing CS embedded in ventral membrane, dorsal membrane embedded with a pair of median sclerotic plates (Figure 8). MPH with MT short, slightly bulged at distal end, about 0.09 times as long as endophallus; membrane of MT randomly distributed with a few round spicules, dorsal membrane at proximal third impressed with a median patch of densely distributed angulate spicules (Figure 8). CT uniformly tubular, curved at middle, about 0.19 times as long as endophallus, proximal two-thirds of membrane uniformly covered with angulate spicules, gradually turning obtuse towards beginning of apical third; apical third dark, densely and compactly adorned with C-shaped spicules, reaching up to proximal half of PB; PB tubular in proximal half, bulged at distal half, as long as MT, uniformly but not densely adorned with C-shaped spicules, gradually turning into U-shaped spicules towards APH. APH funnel shaped, as long as MT, uniformly and closely adorned with stout, broadly U-shaped spicules; junction between PB and APH circumscribed by membranous fringe; apex of APH continued with a membranous tube, bearing RS at distal end. RS about 0.19 times as long as endophallus, uniformly curved in lateral view, composed of two closely appressed, sclerotised plates, of which ventral plate (Figure 9 (b)) dorso-ventrally flattened with lateral sides curved upwards towards dorsal plane distally, broadly encasing dorsal plate; dorsal plate (Figure 9 (a)) made up of two closely approximated inconspicuous rods, forming tubular structure; proximal ends bearing two asymmetrical, falcate tines, one tine being longer than other; apex of longer tine bearing divaricate claw-like projection. ED single, arises medially from distal end of dorsal plate of RS. Female (n = 2) (Figures 2–3). Body length 6.86–6.91 mm, humeral width 2.21–2.26 mm. Similar to male in general appearance, with the following differences. Head with lower eye lobes 1.30–1.33 times as long as genae; mandibles distinctly visible in frontal view. Antennae 1.31 times as long as body. Ratio of lengths of antennomeres: 1.00: 0.25: 1.25: 1.25: 0.95: 0.90: 0.85: 0.80: 0.75: 0.70: 0.70. Pronotum 1.20–1.21 times as wide as long, 0.62–0.65 times as long as humeral width. Elytra 0.72 times as long as body, 3.47–3.55 times as long as pronotum, 2.19–2.26 times as long as humeral width. Last abdominal ventrite robust, dorsally convex, about 0.30–0.32 times as long as length of abdomen, 2.10–2.22 times as long as previous segment; disc medially impressed with a dark brown longitudinal sulcus; apex broadly crescent shaped. Female genitalia (Figures 10–12) with ovipositor (Figure 10 (a)) about 1.10 mm long, in dorsal view thickly covered with adpressed light brown setae at apical third (except coxite lobe and stylus), immediately followed by compactly disposed cells, in scale-like arrangement throughout basal two-thirds except outer margin on each side, which is randomly distributed with a few circular punctures. Coxite lobe light brown, randomly covered with circular punctures except at apex; apex of coxite lobe in dorsal view (Figure 10 (b)) transversely impressed with a single row of closely congregated circular punctures with six setae arising from them, outer setae on either side longer and pointed, remaining setae placed between them, shorter, subequal to each other and obtusely pointed. Stylus dome-shaped, red brown, continuous with coxite lobe; basal portion of stylus impressed with a few remotely distributed punctures; apex of stylus bears a single seta arising from associated puncture. Vaginal plates flap shaped, weakly sclerotised, basally red brown. Bursa copulatrix (Figure 12) elongate, basal two-thirds tubular and bi-sinuate, apical third distinctly capitate. Spermathecal duct distinctly longer than spermatheca, enters bursa copulatrix at apical third, uniformly tubular, with its distal end slightly curved. Spermatheca (Figure 11) arise on spermathecal duct separately, before spermathecal gland, red brown with basal end obliquely curved, distinctly moulded into an elongate, U-shaped tubule up to apical third; apex curved, distinctly capitate. Spermathecal gland sac like, basally with a distinctly sclerotised ringed plate giving rise to a short sclerotised tube. Tignum longer than abdomen. In the specimen examined, tignum measured about 4.94 mm in length while abdomen measured about 3.17 mm. Differential diagnosis Glenea vellayaniensis sp. nov. is closely allied to G. pulchella Pascoe, 1858 and G. vestalis Heller, 1934 by the integument colouration, shape of elytra, and yellow hairs covering the body; however, it can be easily distinguished from them by the appendiculate claws (simple claws for G. pulchella and G. vestalis) and distinct shape of the male genitalia, viz. median lobe distinctly curved in lateral view (vs median lobe weakly curved in lateral view in G. pulchella and G. vestalis), tegmen with lateral lobes medium sized and wider (vs tegmen with lateral lobes distinctly elongate and slender in G. pulchella and G. vestalis), basal piece arcuate distally (vs basal piece bifurcated distally in G. pulchella and G. vestalis), ringed part of tegmen constricted near widest portion (vs ringed part of tegmen weakly geniculated in G. pulchella and G. vestalis), manubrium of ringed part hollow, constricted just before basal end, which is short, and abridged by rectangular membrane (vs manubrium of the ringed part closely approximated from middle, continued to distal end as a slender rod in G. pulchella and G. vestalis), median arm of spiculum gastrale slightly longer than lateral arms (vs median arm of spiculum gastrale distinctly longer than lateral arms in G. pulchella and G. vestalis) and RS composed of two closely appressed, sclerotised plates, of which ventral plate is dorso-ventrally flattened to encase dorsal plate, while dorsal plate is made up of two closely approximated inconspicuous rods, forming tubular structure; proximal ends bear two asymmetrical, falcate tines, one tine being longer than other; apex of longer tine bearing divaricate claw like projection (vs RS without any modifications as previous but made up of 4 rods in G. pulchella and 3 rods in G. vestalis). In female genitalia, spermatheca with stalk strongly moulded into U-shaped tubule (vs stalk slightly curved basally in G. pulchella and G. vestalis). It is also similar to Bifidunguiglenea gestroi (Gahan, 1894) in the integument colouration, body shape and yellow-haired maculae, but can be easily distinguished from the latter by the following characters: claws appendiculate (vs claws bifid in B. gestroi); male genitalia with median lobe distinctly curved in lateral view (vs median lobe indistinctly curved in lateral view in B. gestroi); tegmen with lateral lobes medium sized and wider (vs lateral lobes distinctly short and stout in B. gestroi) lateral lobes separated and ventral face sparsely covered with randomly distributed suberect setae (vs lateral lobes confluent except apex, ventral face densely covered with suberect setae in B. gestroi); ringed part of tegmen constricted near widest portion (vs ringed part of tegmen weakly geniculated in B. gestroi); manubrium of ringed part hollow, constricted just before basal end; basal end short, abridged by rectangular membrane (vs manubria of the ringed part joined with each other at basal third, continued to basal end as short, slender rod in B. gestroi); tergite VIII with apical margin truncated (vs apical margin of tergite VIII angulately projected at middle in B. gestroi); female genitalia with stalk of spermatheca strongly moulded into U-shaped tubule (vs spermatheca with stalk nearly straight in B. gestroi). Etymology The name refers to the type locality of the species, Vellayani campus of the Kerala Agricultural University, situated on the banks of the Vellayani lake, on the outskirts of Trivandrum, in the capital city of Kerala, India. Life history All three specimens were collected by the blue light of Actinic BL TL 8 W tubes. Distribution India (Kerala). Remarks on generic affinity Glenea vellayaniensis sp. nov. is an atypical member of the genus Glenea because of the appendiculate female claws. Claws vary greatly between the males of Glenea spp. (Gahan 1897; Lin et al. 2009b; Lin and Yang 2011), but all of them have simple claws in the females. When the female claws are not simple, they are placed in their own genus in most cases (Lin et al. 2009a; Lin and Tavakilian 2012). The genera Eumecocera Solsky, 1871 and Pareutetrapha Breuning, 1952 have appendiculate claws in both male and female. However, the new species can not be combined with any of these genera because of the presence of a lateral elytral carina, a truncated elytral apex, and distinctly different male genitalia. Meanwhile, some members currently placed in the genus Glenea also have appendiculate claws in both sexes, such as G. lineatocollis Thomson, 1860 and G. tenuilineata Thomson, 1879. However, the new species differs from them not only by morphological characters such as elytral shape, colour and haired pattern, but also by the female genitalia with spermathecal gland originating from a distinctly sclerotised ringed plate. The new species might indicate a closer relationship with the two Glenea spp. treated below, which have simple claws, and female genitalia with spermathecal gland originating from a distinctly sclerotised ringed plate. As the taxonomic complexity of the genus Glenea remains unresolved, we temporarily place the new species within the genus Glenea sensu lato, and do not propose a new generic taxon here.Published as part of Hiremath, Sangamesh R. & Lin, Mei-Ying, 2021, Description of two new species of Glenea Newman, 1842 from southern India and reinstatement of Glenea vestalis Heller, 1934 (Coleoptera: Cerambycidae: Lamiinae: Saperdini), pp. 205-245 in Journal of Natural History 55 (3 - 4) on pages 208-217, DOI: 10.1080/00222933.2021.1900442, http://zenodo.org/record/547373

Special Coordinates Associated With Recursive Forward Dynamics Algorithm for Open Loop Rigid Multibody Systems

The recursive forward dynamics algorithm (RFDA) for a tree structured rigid multibody system has two stages. In the first stage, while going down the tree, certain equations are associated with each node. These equations are decoupled from the equations related to the node’s descendants. We refer them as the equations of RFDA of the node and the current paper derives them in a new way. In the new derivation, associated with each node, we recursively obtain he coordinates, which describe the system consisting of the node and all its descendants. The special property of these coordinates is that a portion of the equations of motion with respect to these coordinates is actually the equations of RFDA associated with the node. We first show the derivation for a two noded system and then extend to a general tree structure. Two examples are used to illustrate the derivation.While the derivation conclusively shows that equations of RFDA are part of equations of motion, it most importantly gives the associated coordinates and the left out portion of the equations of motion. These are significant insights into the RFDA

Static balancing of a four-bar linkage and its cognates

Motivated by the need to statically balance the inherent elastic forces in linkages, this paper presents three techniques to statically balance a four-bar linkage loaded by a zero-free-length spring attached between its coupler point and an anchor point on the ground. The number of auxiliary links and balancing springs required for the three techniques is less than or equal to that of the only technique currently in the literature. One of the three techniques does not require auxiliary links. In these techniques, the set of values for the spring constants and the ground-anchor point of the balancing springs can vary over a one-parameter family. Thrice as many balancing choices are available when the cognates are considered. The ensuing numerous options enable a user to choose the most practical solution. To facilitate the evaluation of the balancing choices for all the cognates, Roberts-Chebyshev cognate theorem is extended to statically balanced four-bar linkages. (C) 2011 Elsevier Ltd. All rights reserved

Glenea pulchella Pascoe 1858

Glenea pulchella Pascoe, 1858 (Figures 13–18) Glenea pulchella Pascoe, 1858: 260. TL: Malacca. TD: BMNH. Glenea vesta Pascoe, 1866: 260, pl. 28, Figure 3. [Unnecessary new name for Glenea pulchella Pascoe, 1858] Glenea pulchella: Aurivillius 1926: 111 (partim). Glenea (Glenea) pulchella: Breuning 1956a: 195 (partim). Type specimen examined Holotype (Figure 13 (a–e)), ♂, Malacca (BMNH, ex Pascoe Coll. 93–60). Other specimens examined Malaysia: 1 ♀, Bornéo Occ., Pontianak, 1899 (MNHN) (Figure 14); 1 ♀, Sarawak (MNHN, Museum Paris Coll. H.W. Bates 1952, ex Musaeo, H.W. Bates 1892); 3 ♂♂ 8 ♀♀, Sandakan Borneo, Baker (NMNH); 1 ♀, Sabah, Mt. Trus-Madi, 18 March 2011, local coll. (DHCO); 1 ♀, Sabah Crocker Range, vic. Trus Madi, 13 March 2000, local coll. (DHCO); 1 ♀, Sabah Crocker Range, April 1998, local coll. (DHCO); 1 ♂, Borneo (IRSNB, ex Coll. Nonfried); 1 ♀, Borneo (IRSNB, ex Coll. F. de Moffaris); 1 ♀, Borneo, Pontanak (NHMB, ex FREY); 2 ♀♀, Borneo Occ. Pontianak, 1899 (MNHN); 1 ♂, Borneo, 1891, W. Doherty (MNHN, ex Coll. R. Oberthür, 1952); 1 ♀, Kuching, 1902 (MHNL, ex collection P. Lepesme); 1 ♀, Borneo occ., Pontianak, 1899 (MHNG); 4 ♀♀, Borneo occ., Pontianak, 1899 (MNHN). Singapore 2 ♂♂, Singapore, coll. Wallace (MNHN, ex Musaeo James Thomson); 2 ♂♂, Singapore (MNHN); 1 ♀, Singapore (BMNH); 1 ♀, Singapore (MNHN, ex Musaeo Mniszech). Description complementary to Pascoe (1858) and Breuning (1956a). Male: length: 8.8–10.3 mm, humeral width: 2.6–3.1 mm. Female: length: 11.3–13.4 mm, humeral width: 3.6–4.3 mm. Both male and female with simple claws. Male genitalia (Figures 15–16) Tegmen length about 2.6 mm; lateral lobes long and slender, each about 1.0 mm long and less than 0.1 mm wide, apex covered with short, reddish brown setae; basal piece bifurcated distally; median lobe plus median struts slightly curved, shorter than tegmen (11:13); the median struts about 2/3 of the whole median lobe in length; dorsal plate subequal to ventral plate; ventral edge of median orifice round; median foramen hardly elongated; internal sac 2 times longer than combined length of median lobe and median struts, with 2 pairs of basal armature and 4 rods; each rod about 1.0 mm, shorter than half of tegmen. Tergite VIII trapeziform, apex truncated, with short setae. Length of ventrite IX subequal to ringed part of tegmen. Female genitalia (Figures 17–18) Spermatheca rounded, with a moderately long and curved stem at its base. Spermathecal gland originating from a distinctly sclerotised ringed plate (Figure 17). Tignum much longer than abdomen. Tignum 8.8 mm for an adult with a 5.3 mm long abdomen in ventral view. Diagnosis Glenea pulchella differs from G. vellayaniensis sp. nov. by colour and haired maculae in the following body regions: (1) scape and antennomere II dark brown to black (vs scape and antennomere II reddish brown in G. vellayaniensis sp. nov.); (2) sublateral macula on pronotum made up of yellow hairs with straight inner margin (vs sublateral macula on pronotum made of yellow hairs intermixed with creamy white hairs with proximally concave inner margin in G. vellayaniensis sp. nov.); (3) basal elytral yellow-haired maculae semicircular (vs basal elytral yellow-haired maculae bean-shaped in G. vellayaniensis sp. nov.); (4) middle elytral yellow-haired maculae oval, without small spots posteriorly (vs median maculae on elytra transversely oval with small spots posteriorly in G. vellayaniensis sp. nov.); (5) elytral apex not covered by yellow hairs, but last maculae located before apex (vs elytral apex covered with yellow haired maculae in G. vellayaniensis sp. nov.). Distribution Malaysia, Singapore. Remarks Pascoe (1866: 260) wrote ‘I have altered the specific name pulchella, it having been previously used by Hope’. And Pascoe gave the species the new name ‘ Glenea vesta ’. Pascoe (1867: 370) wrote ‘ Glenea pulchella Hope, sec. J. Thomson, Ess. & c., p. 58’ from Sarawak. We checked page 58 of Thomson (1857) and found nothing related to ‘ Glenea pulchella Hope’; then we checked page 58 of Thomson (1860), and there it was written ‘ Glenea pulchella, Hope Syn.: G. conspuncta, Melly’. However, ‘Hope’s species was not described before 1860’ (Aurivillius 1926: 111). ‘ Glenea pulchella Hope’ described by Pascoe (1867) was renamed Glenea pascoei Aurivillius, 1923, while ‘ Glenea pulchella Hope’ described by Thomson (1860) from Sylhet was renamed Glenea pulchra Aurivillius, 1926. Glenea pulchella Pascoe, 1858 is the earliest name, and therefore the new name ‘ Glenea vesta ’ is not required. Breuning (1956a) treated G. vestalis Heller, 1934 as a morph and described several morphs (infrasubspecific). However, his ‘morphs’ are good species. Mukhopadhyay and Biswas (2000) reported the distribution range of G. pulchella as India: Meghalaya, Bangladesh, Burma; while Mitra et al. (2016) mentioned India: Karnataka, Manipur, Meghalaya, Sikkim, Tamil Nadu, West Bengal. These distribution records are not reliable, based on neither specimens nor trustable identifications. The first author inquired for supportive material from the Zoological Survey of India (ZSI), Kolkata; however, there are no specimens of G . pulchella in the collection. The known localities of this species are, to our knowledge, limited to Malaysia and Singapore.Published as part of Hiremath, Sangamesh R. & Lin, Mei-Ying, 2021, Description of two new species of Glenea Newman, 1842 from southern India and reinstatement of Glenea vestalis Heller, 1934 (Coleoptera: Cerambycidae: Lamiinae: Saperdini), pp. 205-245 in Journal of Natural History 55 (3 - 4) on pages 217-221, DOI: 10.1080/00222933.2021.1900442, http://zenodo.org/record/547373

Glenea vestalis , Heller 1934

Glenea vestalis Heller, 1934 stat. reinstated (Figures 19–25) Glenea vestalis Heller, 1934: 284, Figure 2. TL: Philippines. TD: SMTD. Glenea pulchella: Aurivillius 1926: 111 (partim). Glenea (Glenea) pulchella: Breuning 1956a: 195 (partim). Glenea (Glenea) pulchella m. postmediopunctata Breuning, 1956a: 196. [Unavailable name, infrasubspecies from Tonkin, Vietnam] Glenea (Glenea) pulchella m. preapiceconjuncta Breuning, 1956a: 197. [Unavailable name, infrasubspecies from Ceram, Indonesia] Glenea (Glenea) pulchella m. transversevittata Breuning, 1956a: 197. [Unavailable name, infrasubspecies from Fundortangabe] Glenea (Glenea) pulchella m. vestalis: Breuning 1956a: 197. Glenea (Glenea) pulchella: Hüdepohl 1996: 18. [Misidentification] Type specimen examined Holotype (Figure 19 (a–c)), ♀, Philippines, Arorey, 1923.VIII (SMTD). Other Specimens examined Philippines: 1 ♂, ‘paratype’ of Glenea (Glenea) pulchella m. postmediopunctata Breuning, 1956, Dapitan, Mindanao, Baker (MHNL, ex collection P. Lepesme); 1 ♂, ‘paratype’ of Glenea (Glenea) pulchella m. postmediopunctata Breuning, 1956, Zamboanga, Mindanao, Baker (MHNL, ex collection P. Lepesme); 1 ♀, ‘paratype’ of Glenea (Glenea) pulchella m. postmediopunctata Breuning, 1956, Surigao, Mindanao, Baker (NHMB (Frey)); 1 ♂, Philippines (BMNH); 1 ♂, 2 ♀♀, Zamboanga Mindanao, Baker (NMNH); 2 ♀♀, Island Samar, Baker (NMNH); 4 ♂♂, 2 ♀♀, Kolambugan, Mindanao, Baker (NMNH); 1 ♂, 1 ♀, Davao Mindanao, Baker (NMNH); 2 ♂♂, 2 ♀♀, Mt. Makiling, Luzon, Baker (NMNH); 2 ♂♂, 4 ♀♀, Dapitan, Mindanao, Baker (NMNH); 1 ♂, 1 ♀, Butuan Mindanao, Baker (NMNH); 1 ♀, Surigao, Mindanao (NMNH, Tippmann Coll. ’57, 213112); 2 ♀♀, Philippines, Ch Semper (MNHN); 1 ♂, Mindanao (Figure 20 (a,b), MNHN); 3 ♀♀, Mindanao, 1903–1904, J. Waterstradt (MNHN); 1 ♀, Philippines, N. Luzon, Cagayan, Sta. Ana, June 2014, local coll. (DHCO). Malaysia 1 ♀, Java (Meuwen Bay) (MNHN); 2 ♀♀, ‘paratypes’ of Glenea (Glenea) pulchella m. preapiceconjuncta Breuning, 1956, Borneo, Sandakan, Baker (NHMB (Frey)); 1 ♀, Malacca, Perak, W. Doherty (MNHN). Indonesia 1 ♀ (Figure 21 (a,b)), ‘type’ of Glenea (Glenea) pulchella m. preapiceconjuncta Breuning, 1956, Moluccas, Ceram (= Moluques, Seram) (BMNH, ex Fry Coll, 1905.100); 1 ♀, Maluku, Seram, 35 km E Pasahari, Unit O, 24–30 October 1998, leg. J. Horák (DHCO). Vietnam 1 ♀ (Figure 22 (a,b)), ‘type’ of Glenea (Glenea) pulchella m. postmediopunctata Breuning, 1956, Tonkin, Hoa-Binh, A. de Cooman (MHNL, ex Coll. Lepesme, 2002, ex Coll. J. Clermont). Description complementary to Heller (1934) and Breuning (1956a). Male genitalia (Figures 23–24) Tegmen length about 3.5 mm; lateral lobes extremely long and slender, each about 1.8 mm long and 0.05 mm wide, apex covered with short, reddish brown setae; basal piece bifurcated distally; median lobe plus median struts slightly curved, much shorter than tegmen (22:35); median struts about two-thirds of whole median lobe in length; dorsal plate slightly shorter than ventral plate; ventral edge of median orifice slightly pointed; median foramen elongated; internal sac about 3 times as long as median lobe plus median struts, with four pieces of basal armature and three rods; rods about 1.0 mm, shorter than one-third of tegmen. Tergite VIII elongate, U-shaped with its apical margin weakly notched in middle, integument with short setae. Ventrite IX subequal to ringed part of tegmen in length. Female genitalia (Figure 25): Spermatheca elongate, with its stalk curved at base and capsule oval. Spermathecal gland originating from a distinctly sclerotised ringed plate (Figure 25). Tignum much longer than abdomen. In our observation, tignum 8.5 mm for an adult with a 5.3 mm long abdomen in ventral view. Diagnosis This species is very similar to G. pulchella Pascoe at first glance, with body reddish brown and similar yellow-haired maculae. However, they differ from each other in the absence vs presence of the small spot at the centre of apical half. Male genitalia exhibit distinct differences also: lateral lobes shorter than half of tegmen and apex of tergite VIII truncated in G. pulchella (Figures 15 and 16) vs lateral lobes subequal to half of tegmen and apex of tergite VIII weakly notched at middle in G. vestalis (Figures 23 and 24). Distribution Philippines, Malaysia, Indonesia, Vietnam. Remarks Breuning (1956a) treated G. vestalis as a morph of G. pulchella, and subsequent authors considered them synonyms (Hüdepohl 1996; Tavakilian and Chevillotte 2020). However, they are two distinct species, and G. vestalis is herein reinstated from synonymy with G. pulchella. Aurivillius (1926: 111) wrote: ‘Specimens from Mindanao have a small sulphur yellow lateral dot behind the middle of elytra; this dot is wanting in specimens from Borneo and Malacca but still more developed in a specimen from Ceram’. Examination of specimens from these localities by the second author revealed that specimens referred to as having a ‘small sulphur yellow lateral dot’ behind the middle of the elytra, from Philippines and Ceram (now Indonesia, Maluku, Seram), are G. vestalis, while the specimens from Borneo and Malacca, in which ‘this dot is wanting’, are G. pulchella. Breuning (1956a) described three morphs, which are all infrasubspecific. The second author examined the ‘type’ and ‘paratypes’ of these morphs; the ‘type’ of Glenea (Glenea) pulchella m. preapiceconjuncta Breuning, 1956 (Figure 21 (a,b)) from ‘ Insel Ceram im Britischen Museum’, and the ‘type’ of Glenea (Glenea) pulchella m. postmediopunctata Breuning, 1956 (Figure 22 (a,b)) from ‘ Tonkin: Hoa-Binh in coll. Lepesme’ are both females and are both considered Glenea vestalis Heller, 1934 based on the presence of a postmedial, sulphur yellow lateral dot on the elytra. The ‘type’ of Glenea (Glenea) pulchella m. transversevittata Breuning, 1956, based on ‘ein female ohne Fundortangabe in der Sammlung Itzinger’, could not be examined; however, in all probability it belongs to G. vestalis, since Breuning (1956a: 197) compared it with m. postmediopunctata and arranged it between m. preapiceconjuncta and m. vestalis Hell.Published as part of Hiremath, Sangamesh R. & Lin, Mei-Ying, 2021, Description of two new species of Glenea Newman, 1842 from southern India and reinstatement of Glenea vestalis Heller, 1934 (Coleoptera: Cerambycidae: Lamiinae: Saperdini), pp. 205-245 in Journal of Natural History 55 (3 - 4) on pages 221-225, DOI: 10.1080/00222933.2021.1900442, http://zenodo.org/record/547373

A Note on the Diagonalizability and the Jordan Form of the 4×4 Homogeneous Transformation Matrix

The 4x4 homogeneous transformation matrix is extensively used for representing rigid body displacement in 3D space and has been extensively used in the analysis of mechanisms, serial and parallel manipulators, and in the field of geometric modeling and computed aided design. The properties of the transformation matrix are very well known. One of the well known properties is that a general 4x4 homogeneous transformation matrix cannot be diagonalized, and at best can be reduced to a Jordan form. In this paper, we show that the 44 homogeneous transformation matrix can be diagonalized if and only if displacement along the screw axis is zero. For the general transformation with nonzero displacement along the axis, we present an explicit expression for the fourth basis vector of the Jordan basis. We also present a variant of the Jordan form which contains the motion variables along and about the screw axis and the corresponding basis vectors which contains the information only about the screw axis and its location. We present a novel expression for a point on the screw axis closest to the origin, which is then used to form a simple choice of basis for different forms. Finally, the theoretical results are illustrated with a numerical example