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This paper introduces the concept of isomorphism into the study of metamorphic mechanisms and presents the design of the isomorphic metamorphic mechanism, in which the structure is the same but the shape topology is different. A novel plane-space polyhedral metamorphic mechanism governed by the edge forming principle is developed. This mechanism is able to achieve the structural transformation between plane topology and space topology, and it has broad prospects for engineering application. The polyhedral metamorphic mechanism can be evolved into isomorphic mechanisms, like the spherical metamorphic mechanism and conical metamorphic mechanism, according to the scale relation between links. The evolution principle and movement conditions of the isomorphic mechanism are analyzed. The position and velocity of joints of novel plane-space isomorphism metamorphic mechanism and the workspace of these mechanisms are compared and analyzed using screw theory, and the configuration expanded analysis of novel plane-space metamorphic mechanism is performed. Finally, potential engineering applications are listed. The research results provide a reference for the reasonable choice of application configuration for such mechanisms.

In this paper, we discuss the initial value problem of fractional differential equations in-volving Riemann-Liouville differentialoperators. By means of the mixed monotoneoperator theory, we obtain the existence and uniquenessof the solutions to the initial value problem,and an exampleis givento illustrate the main result.

Pseudechiniscus chengi sp. nov. (Table 2, Figs. 4–7) Material examined. Holotype (slide number: xnc02001) and four paratypes (slide numbers: xnc02002, xnc02005, xnc02011, and xnc02013). Type locality. Same as Bryochoerus liupanensis sp. nov. Type depository. Same as Bryochoerus liupanensis sp. nov. Diagnosis. Colour brown. Eye spots present. Cephalic papilla dome-shaped. Cirrus A short. Frontal plate faceted. Median plates undivided. Third median plate present, but sometimes weakly developed or not visible. Pseudosegmental plate with longitudinal median fold, the posterior margin of the pseudosegmental plate without any projection. Terminal plate with well-developed incisions. All plates and upper part of all legs with cuticular sculpture composed of round dots differing in size. Striae absent between dots. Lateral intersegmental plates absent. Ventral side of the body without plate. Papilla present on legs IV. Dentate collar absent on legs IV. Very small spur present on the internal claws on all legs. Description. Body colour brown. Eyes present. Head tapered and long at the rostral end, body slender (Fig. 4 a). Apart from head appendages, only lateral appendages cirri A present. Cirrus A short. Primary clava is a papilla. The cephalic papilla dome-shaped, short and thick, well developed (Fig. 4 b). Stylets present, stylet supports absent (or not visible after slide preparation), buccal tube long and narrow, pharyngeal bulb round (Fig. 5 b). Head plate with W-shaped fold, two short longitudinal ridges connected to the angles of the W-shaped fold respectively. Anterior part of the scapular plate with a short longitudinal middle ridge, posterior part of scapular plate transversely divided into four parts. Dorsal plates contain first undivided median plate, first paired plates, second undivided median plate, second paired plates, pseudosegmental plate and the terminal plate, third median plate present (holotype and xnc02005) (Fig. 4 a), but sometimes weakly developed or not visible (xnc02002, xnc02011 and xnc02013) (Fig. 5 a), if present, rhombic and undivided. Pseudosegmental plate with a longitudinal median fold. Lobes, spines, or any other projections on posterior margin of the pseudosegmental plate absent. Terminal plate with two well developed incisions on each side. Lateral intersegmental plates absent. All dorsal plates have a dense and regular ornamentation comprised of dots, dot round-shaped and differing in size, dots on the paired plates larger than the ones on unpaired plates (Figs. 4 a, 6). Diameter of the largest dot up to 0.86 μm. Ventral side of body without plates. All legs without spines. Fourth pair of legs without dentate collar but with a small papilla (Fig. 7 a). The upper part of all legs covered with plates and ornamentation composed of dots similar to those on dorsal plates (Fig. 7 a), but smaller. A very thin spur pointed backward the claw base is present on internal claws of all legs (Figs. 4 b, 7b). Etymology. This species is dedicated to Prof. Guangxu Cheng, President of Shaanxi Normal University, for his contributions to the development of our university. Structure xnc02001 xnc02002 xnc02005 xnc02011 xnc02013 female female female female female Differential diagnosis. Pseudechiniscus chengi sp. nov. is similar to Pseudechiniscus bartkei Węglarska 1962 (North Viet Nam), Pseudechiniscus gullii (Pilato & Lisi 2006) (Southern Mexico), Pseudechiniscus novaezeelandiae novaezeelandiae (Richters 1908) (New Zealand), Pseudechiniscus quadrilobatus Iharos 1969 (Viet Nam), Pseudechiniscus santomensis Fontoura et al. 2010 (Democratic Republic of São Tomé and Príncipe), Pseudechiniscus spinerectus Pilato et al. 2001 (Ecuador), and Pseudechiniscus yunnanensis Wang 2009 (Yunnan, China), in having a similar cuticular sculpture on the dorsal plates. The new species differs from the above species mainly by lacking the striae between cuticular granules. In addition, Pseudechiniscus chengi sp. nov. differs from P. bartkei in lacking the bilobed process on the caudal margin of the pseudosegmental plate; and from P. gullii in lacking the triangular lobe on the posterior margin of the pseudosegmental plate, and in having spur on the internal claws on all legs. The new species differs from P. n. novaezeelandiae by the undivided median plates 1 and 2, and in lacking spines on the caudal margin of the pseudosegmental plate; and from P. quadrilobatus in lacking the uplifted lobes on the posterior margin of the dorsal plates, and pseudosegmental plate along the median line. Pseudechiniscus chengi sp. nov. it differs from P. santomensis in lacking the tiny projections on the caudal margin of the pseudosegmental plate, and by undivided pseudosegmental plate; and differs from P. spinerectus in lacking the triangular spines on the caudal margin of the pseudosegmental plate. The new species differs from P yunnanensis in lacking the triangular spines on the caudal margin of the pseudosegmental plate, and in having notches on the terminal plate.

Bryochoerus liupanensis sp. nov. (Table 1, Figs. 1–3) Type material. Holotype: Female, slide number: xnc02006. Type locality. 35.36043N, 106.31239E (35°21′37.55″ N, 106°18′44.60″E), 1,986m asl, the Liupanshan National Forest Park, Jingyuan County, Ningxia Hui Autonomous Region, China. Paratypes: slide number: xnc03003, xnc03005, xnc03006, xnc03009. Type repository. Li’s tardigrade collection, Molecular Ecology, Department of Biology, College of Life Sciences of Shaanxi Normal University, China. Diagnosis. Apart from the head appendages including cirrus internus, cephalic papillae and cirrus externus, only lateral cirrus A with clava present; dorsal plates and lateral plates with double sculpture including large bright roundish granule-like dots and small dark roundish dots; median plates 1 and 2 divided transversely into four parts, median plate 3 divided transversely into three parts; two lateral plates on each side of all median plates, 12 in total; paired plates with a transverse smooth band; terminal plate with two longitudinal ridges which divided the terminal plate into three parts, terminal plate without notches; ventral side of body without plates or platelets; papilla not visible and dentate collar absent on legs IV; small spurs present on internal claws on all legs. Description. Colour orange. Eye spots absent or not visible after slide preparation. Apart from head appendages, including cirrus internus, cirrus externus and cephalic papillae (secondary clava), only lateral cirrus A with clava (primary clava) are present; cephalic papillae drop-shaped; stylet supports not visible, pharyngeal bulb roundish; dorsal plates comprise of head plate, scapular plate, first median plate, first paired plates, second median plate, second paired plates, third median plate, and terminal plate; all median plates divided transversely, median plate 1 and median plate 2 divided into four parts, while median plate 3 divided into three parts, the normal parts of all median plates are the same as Bryodelphax species, however all median plates are followed with two intersegmental plates, two lateral plates present on each side of all median plates, 12 in total, two paired plates with a transverse smooth band, terminal plate with two longitudinal ridges which divide terminal plate into three parts, terminal plate without incisions; all plates, including dorsal plates and lateral plates, with “double sculpture”, including large bright roundish pores and small dark roundish dots that are pillars within the cuticle, pores are scarce and distributed loosely whereas dark dots are arranged regularly and densely (Figs. 1 a, 2); ventral side without plate or platelets (Fig. 1 b). Spine on legs I and papilla on legs IV not visible under light microscope. Dentate collar absent on legs IV. Internal claws on all legs with small spur, external claws spurless (Fig. 3 a), the upper part of all legs were covered with plate with sculpture of small dots (Fig. 3 b). Eggs unknown. For measurements see Table 1. Remarks. Please see Michalczyk & Kaczmarek 2006 or Kaczmarek et al. 2012 for more information on the anatomy of ‘double sculpturing’. Whether the spine on legs I and papilla on legs IV are indeed absent, has to be confirmed by SEM observations in the future. Structure xnc02006 xnc03003 xnc03005 xnc03006 xnc03009 female female female female female Etymology. The new species is named after the type locality. Differential diagnosis. The monotypic genus Bryochoerus contained only the nominate species Bryochoerus intermedius. There are three subspecies in B. intermedius. They are B. i. intermedius (Murray, 1910), B. i. hawaiicus (Thulin, 1928) and B. i. laevis (Marcus, 1936) (Kristensen 1987; Ramazzotti & Maucci 1983). Bryochoerus liupanensis sp. nov. differs from Bryochoerus intermedius intermedius in having orange colour instead of colourless, or yellowish, or else greenish-yellow as in B. i. intermedius; a different cuticular sculpture; presence of lateral plates; lacking papilla and dentate collar on legs IV; and presence of spurs on the internal claws of all legs. The new species differs from B. i. hawaiicus in having different cuticular sculpture; presence of lateral plates; and presence of spurs on the internal claws of all legs. Bryochoerus liupanensis sp. nov. differs from B. i. laevis in having a different cuticular sculpture; presence of lateral plates in a different shape; a facetted terminal plate; lacking spine on the first pair of legs; and lacking papilla and dentate collar on legs IV.

Metamorphic mechanism will result in impact when it is changing from one configuration to the next. Consequently, the internal impact force will bring about resonance for the mechanism. Therefore, it is necessary to study the nonlinear dynamics of the metamorphic mechanism when it is changing configuration. The controllable metamorphic palletizing robot mechanism is investigated in this paper. Based on the nonlinear dynamic model of the novel controllable metamorphic palletizing robot mechanism system of all configurations under the actual operating, the multiscale method is applied to analyze the nonlinear super harmonic vibration and to solve analytical solution of the mechanism when it is changing configuration and suffering internal impact. And numerical solution of the nonlinear dynamic model is solved by newmark method. Finally, dynamic simulation analysis is completed through example study. Time-domain and frequency-domain dynamic responses under the influence of super harmonic resonance when the mechanism is changing configuration and suffering internal impact are obtained. The research achievement of this paper provides fundamental references for nonlinear vibration study of controllable metamorphic mechanism.