Spiral Segments Research Articles

Practical and flexible path planning for car-like mobile robot using maximal-curvature cubic spiral

This paper presents a nonholonomic path planning method, aiming at taking into considerations of curvature constraint, length minimization, and computational demand, for car-like mobile robot based on cubic spirals. The generated path is made up of at most five segments: at most two maximal-curvature cubic spiral segments with zero curvature at both ends in connection with up to three straight line segments. A numerically efficient process is presented to generate a Cartesian shortest path among the family of paths considered for a given pair of start and destination configurations. Our approach is resorted to minimization via linear programming over the sum of length of each path segment of paths synthesized based on minimal locomotion cubic spirals linking start and destination orientations through a selected intermediate orientation. The potential intermediate configurations are not necessarily selected from the symmetric mean circle for non-parallel start and destination orientations. The novelty of the presented path generation method based on cubic spirals is: (i) Practical: the implementation is straightforward so that the generation of feasible paths in an environment free of obstacles is efficient in a few milliseconds; (ii) Flexible: it lends itself to various generalizations: readily applicable to mobile robots capable of forward and backward motion and Dubins’ car (i.e. car with only forward driving capability); well adapted to the incorporation of other constraints like wall-collision avoidance encountered in robot soccer games; straightforward extension to planning a path connecting an ordered sequence of target configurations in simple obstructed environment.

Cooperative Obstacle-Avoidance Pushing Transportation of a Planar Object with One Leader and Two Follower Mobile Robots

This paper proposes a cooperative obstacle-avoidance pushing transportation system using one leader and two follower mobile robots. Its usefulness and effectiveness are illustrated and confirmed numerically as well as experimentally. The cooperative obstacle-avoidance pushing transportation control consists of the obstacle configuration measurement phase by the leader mobile robot, the trajectory-planning phase and the pushing transfer control phase by the two follower mobile robots. In the obstacle configuration measurement phase, the leader mobile robot moves by use of the obstacle-avoidance vehicle control method constructed with six infrared sensors and the pattern recognition algorithm, and three waypoints for the trajectory planning of the follower mobile robots are extracted. In the trajectory-planning phase, the two follower mobile robots receive the three modified waypoints from the leader mobile robot through wireless communication systems, and the obstacle-avoidance trajectories by use of cubic spiral and straight-line segments are generated. Then, in the pushing transfer control phase, a planar object is transported with the pushing and constraining forces resulting from the passive compliance mechanisms attached to the follower mobile robots, and the shock is effectively reduced by the passive compliance mechanisms. From the numerical simulation and experimental results using autonomous mobile robots (MK-01X developed by Fuji Heavy Industries Ltd.), it is confirmed that the planar object can be successfully transported by pushing from the start configuration to the goal in spite of the existence of the obstacle.

605 非円形断面NC輪郭加工における工具経路の最適アルキメデス螺線補間法の効果(G.S.設計・工作1,九州支部 第58期総会・講演会)

605 非円形断面NC輪郭加工における工具経路の最適アルキメデス螺線補間法の効果(G.S.設計・工作1,九州支部 第58期総会・講演会)

Embryonic and intracapsular larval development of Plicopurpura pansa (Gould, 1853) (Prosobranchia, Muricidae) under laboratory conditions

The embryonic development of the marine muricid Plicopurpura pansa (Gould, 1853) until hatching is described. Each female spawned about 150 egg capsules in a 10-week period. The egg showed spiral segmentation, followed by gastrulation through epiboly, the formation of a non-typical trochophore and veliger larva. The embryos fed on the egg yolk. Nurse eggs were not observed. In 13% of the egg capsules, different embryonic or larval stages of development were found in the same capsule. At 21–23ºC the intracapsular development was completed with the hatching of planktotrophic veliger larvae after a period of 5 to 8 weeks.

Optimal Interpolation of Archimedes's Spiral for NC Machining of Noncircular Contours

In NC machining of noncircular contours, where cutter is fed along a straight line intersecting perpendicularly the roration axis of work piece, the cutter path usually consists of Archimedes's spiral segments. From machining precision and efficiency point of view, a desired cutter path should be composed of the fewer segments as possible under the condition of satisfying the specified interpolation error limitation. In this paper, an optimal interpolation principle of Archimedes's spiral for planar curves is presented and then a practical algorithm is constructed. The segment number of the cutter path resulted from the algorithm not only is the fewest but also the interpolation accuracy agrees with the specified value. It is also evidenced that the profile error of machined contour corresponding to the cutter path is perfectly controlled within the desired value, i. e. the specified interpolation error value, through detailed analyses. The interpolation results of using the presented algorithm for machining disc cam profile are compared with those obtained by Nishioka's methods (3) . The comparison results sufficiently confirm the validity of the algorithm developed by the authors.

Planar G2 transition curves composed of cubic Bézier spiral segments

In curve and surface design it is often desirable to have a planar transition curve, composed of at most two spiral segments, between two circles. The purpose may be practical, e.g., in highway design, or aesthetic. Cubic Bézier curves are commonly used in curve and surface design because they are of low degree, are easily evaluated, and allow inflection points. This paper generalizes earlier results on planar cubic Bézier spiral segments which were proposed as transition curve elements, and examines techniques for curve design using the new results.

3018 非円形形状加工における工具経路の極座標直線方式補間

In NC machining of non-circular contours, where cutter is fed along a straight line intersecting perpendicularly the rotation axis of work piece, the cutter path usually consists of Archimedes's spiral segments, i.e. the polar straight line segments. From machining precision and efficiency point of view, an optimal interpolation principle and a practical algorithm for planar curves are presented. The segment number of the cutter path resulted from the algorithm is not only the fewest but also the interpolation accuracy agrees with the specified value. The validity of the algorithm is well demonstrated through interpolation results to machining of two disc cam profiles.

Square spiral photonic crystals: robust architecture for microfabrication of materials with large three-dimensional photonic band gaps.

We provide a blueprint for microfabricating photonic crystals with very large and robust three-dimensional photonic band gaps (PBG's). These crystals are based on interleaving polygonal spiral posts and can be efficiently manufactured on a large scale in a one-step process using the recently introduced technique of glancing angle deposition. We classify various families of spiral photonic crystals based on (i) the parent three-dimensional (3D) point lattice to which they are most closely related, (ii) the crystallographic axis of the parent lattice around which the spiral posts wind, and (iii) the set of points of the parent lattice which the spiral arms connect or nearly connect. We obtain optimal geometries for the spiral photonic crystals by detailed mapping of the size and location of the PBG within a multidimensional parameter space which characterizes the shape of each spiral post. For the optimum PBG, the spiral arms and elbows may deviate significantly from the points of the original point lattice. The largest 3D PBG's are obtained for square spiral posts that wind around the [001] axis of diamond (or face centered cubic) lattice and in which the spiral arm segments approximately connect either the fifth or first nearest-neighbor points of the parent lattice. In the case of silicon posts (with a dielectric constant of 11.9) in an air background, whose arm segments nearly connect fifth nearest-neighbor point of the diamond lattice, the full PBG can be as large as 16% of the gap center frequency. For the corresponding air posts in a silicon background, the maximum PBG is 24% of the gap center frequency. We compute both the total electromagnetic density of states and the electromagnetic field distributions near the PBG. It is suggested the PBG in an optimized structure is highly tolerant to various forms of disorder that may arise during the manufacturing process.

Macrophage-Induced Apoptosis Limits Endovascular Trophoblast Invasion in the Uterine Wall of Preeclamptic Women

Impaired invasion of uteroplacental arteries by extravillous trophoblast cells is a key pathogenic mechanism of preeclampsia. We previously demonstrated that reduced trophoblast invasion into uteroplacental spiral arteries was associated with an excess of macrophages in and around these arteries. To explore the significance of these observations, we correlated the extent of extravillous trophoblast apoptosis in placental bed biopsy specimens with macrophage distribution and studied the effect of macrophages upon trophoblast apoptosis in vitro. Extravillous trophoblast hybrid cells were cocultured with activated macrophages exposed to exogenous tumor necrosis factor α (TNFα), anti-tumor necrosis factor receptor I (TNF-RI), and tryptophan depletion, and the rates of trophoblast apoptosis were measured. Extravillous trophoblast hybrid cells showed increased rates of apoptosis following exposure to exogenous TNFα, with tryptophan depletion, and when cocultured with activated macrophages. The proapoptotic effects of macrophages in vitro were completely inhibited only by simultaneous addition of tryptophan and anti–TNF-RI. Our data indicate that macrophages, residing in excess in the placental bed of preeclamptic women, are able to limit extravillous trophoblast invasion of spiral arterial segments through apoptosis mediated by the combination of TNFα secretion and tryptophan depletion. The mechanisms by which macrophages are activated and recruited to the placental bed are presently unknown but are likely central to the pathogenesis of preeclampsia.

System integrated product design, CNC programming and postprocessing for three-axis lathes

New three-axis CNC turning machines have been installed on shop floors of factories in the last few years. Although the machines are still particularly adapted to cylindrical work, they are also used for non-cylindrical machining. The third axis, C or Y, and separately driven, additional milling cutters have eliminated traditional limitations and opened new machining possibilities, i.e. turning and milling the non-rotational shapes. Even the advanced, integrated CAD/CAM systems do not support the milling and turning processes on three-axis CNC lathes or turning centers. Manual part programming for such machine tools, if available, does not facilitate the integration between design and manufacturing. For accurate part programming on three-axis lathes a new interpolation scheme must be applied, using both spiral segments of Archimedes and circular segments rather than linear segments as applied in CNC milling. Specialized, built-in software developed for the three-axis lathes enables to expand CAD/CAM integration to the same extent as in CNC multi-axis milling. The software includes modified postprocessors for three-axis lathes as well. The integrated processes of design and manufacturing are the most important prerequisites for effective concurrent engineering. In general, it means both better economics and quality of complex products, e.g. shaped rolls for rolling operations, cams and camshafts (non-ruled surfaces included), non-rotational shafts, airscrews, prostheses for total hip replacements, etc.

Magnetic and optical spiral arms in the galaxy NGC 6946

The spiral pattern in the nearby spiral galaxy NGC 6946 has been studied using the wavelet transformation technique, applied to galaxy images in polarized and total non-thermal radio emission at lambda lambda3.5 and 6.2 cm, in broadband red light, in the lambda 21.1 cm H I line and in the optical H alpha line. Well-defined, continuous spiral arms are visible in polarized radio emission and red light, where we can isolate a multi-armed pattern in the range of galactocentric distances 1.5-12 kpc, consisting of four long arms and one short spiral segment. The 'magnetic arms' (visible in polarized radio emission) are localized almost precisely between the optical arms. Each magnetic arm is similar in length and pitch angle to the preceding optical arm (in the sense of galactic rotation) and can be regarded as its phase-shifted image. Even details like a bifurcation of an optical arm have their phase-shifted counterparts in the magnetic arms. The average relative amplitude of the optical spiral arms (the stellar density excess over the azimuthal average) grows with galactocentric radius up to 0.3-0.7 at r similar or equal to5 kpc, decreases by a factor of two at r=5-6 kpc and remains low at 0.2-0.3 in the outer parts of the galaxy. By contrast, the magnetic arms have a constant average relative amplitude (the excess in the regular magnetic field strength over the azimuthal average) of 0.3-0.6 in a wide radial range r=1.5-12 kpc. We briefly discuss implications of our findings for theories of galactic magnetic fields.

Estimated flow resistance increase in a spiral human coronary artery segment.

Coronary flow estimates were made for a spiral coronary artery segment (identified from a post-mortem replica casting) by using a modified Dean number based on the approximate coil radius of curvature, as suggested earlier. The estimates were found to correlate experimental pressure drop data for helical coiled tubes. Over a physiological range of mean Reynolds numbers from 100 to 400 for blood flow through main coronary arteries, estimates of the flow resistance increase relative to a straight lumen segment ranged from about 20 to 80 percent, and were of similar magnitude to those found in a flow study in a sinuous coronary vessel segment with no spiral.

ECG-correlated image reconstruction from subsecond multi-slice spiral CT scans of the heart.

Subsecond spiral computed tomography (CT) offers great potential for improving heart imaging. The new multi-row detector technology adds significantly to this potential. We therefore developed and validated dedicated cardiac reconstruction algorithms for imaging the heart with subsecond multi-slice spiral CT utilizing electrocardiogram (ECG) information. The single-slice cardiac z-interpolation algorithms 180 degrees CI and 180 degrees CD [Med. Phys. 25, 2417-2431 (1998)] were generalized to allow imaging of the heart for M-slice scanners. Two classes of algorithms were investigated: 180 degrees MCD (multi-slice cardio delta), a partial scan reconstruction of 180 degrees + delta data with a < phi (fan angle) resulting in effective scan times of 250 ms (central ray) when a 0.5 s rotation mode is available, and 180 degrees MCI (multi-slice cardio interpolation), a piecewise weighted interpolation between successive spiral data segments belonging to the same heart phase, potentially providing a relative temporal resolution of 12.5% of the heart cycle when a four-slice scanner is used and the table increment is chosen to be greater than or equal to the collimated slice thickness. Data segments are selected by correlation with the simultaneously recorded ECG signal. Theoretical studies, computer simulations, as well as patient measurements were carried out for a multi-slice scanner providing M = 4 slices to evaluate these new approaches and determine the optimal scan protocol. Both algorithms, 180 degrees MCD and 180 degrees MCI, provide significant improvements in image quality, including extremely arythmic cases. Artifacts in the reconstructed images as well as in 3D displays such as multiplanar reformations were largely reduced as compared to the standard z-interpolation algorithm 180 degrees MLI (multi-slice linear interpolation). Image quality appears adequate for precise calcium scoring and CT angiography of the coronary arteries with conventional subsecond multislice spiral CT. It turned out that for heart rates fH > or = 70 min(-1) the partial scan approach 180 degrees MCD yields unsatisfactory results as compared to 180 degrees MCI. Our theoretical considerations show that a freely selectable scanner rotation time chosen as a function of the patient's heart rate, would further improve the relative temporal resolution and thus further reduce motion artifacts. In our case an additional 0.6 s mode besides the available 0.5 s mode would be very helpful. Moreover, if technically feasible, lower rotation times such as 0.3 s or even less would result in improved image quality. The use of multi-slice techniques for cardiac CT together with the new z-interpolation methods improves the quality of heart imaging significantly. The high temporal resolution of 180 degrees MCI is adequate for spatial and temporal tracking of anatomic structures of the heart (4D reconstruction).

Structure in the Neutral Hydrogen Disk of the Spiral Galaxy IC 342

We present 38''resolution Very Large Array 21 cm continuum and H I line emission observations of the spiral galaxy IC 342, at an adopted distance of 2 Mpc. Kinematic evidence exists for a m = 2 spiral density wave in the inner disk with a corotation radius located at 4 kpc and a possible four-arm pattern in the outer disk. On smaller scales, outside of the central depression in H I column density, H I is organized into a complex pattern of relatively short (∼2–5 kpc), interconnected, spiral arm segments. Numerous "holes" are distributed throughout the H I disk. By considering the effects of shear, structures that are not self-gravitating, such as holes and voids, cannot be long-term phenomena. The timescale, combined with the total energy required to evacuate holes, leads us to reject wind and supernovae origins for the large-scale pattern of H I holes in IC 342. Gravitational instabilities in the disk form on a timescale that is short compared with the rotation period of the disk. The pattern of H I spiral arm segments exists on a scale that is consistent with their being material arms that result from gravitational instabilities. The H I cavities are a natural remnant of the process.

Advanced single-slice rebinning in cone-beam spiral CT.

To achieve higher volume coverage at improved z-resolution in computed tomography (CT), systems with a large number of detector rows are demanded. However, handling an increased number of detector rows, as compared to today's four-slice scanners, requires to accounting for the cone geometry of the beams. Many so-called cone-beam reconstruction algorithms have been proposed during the last decade. None met all the requirements of the medical spiral cone-beam CT in regard to the need for high image quality, low patient dose and low reconstruction times. We therefore propose an approximate cone-beam algorithm which uses virtual reconstruction planes tilted to optimally fit 180 degrees spiral segments, i.e., the advanced single-slice rebinning (ASSR) algorithm. Our algorithm is a modification of the single-slice rebinning algorithm proposed by Noo et al. [Phys. Med. Biol. 44, 561-570 (1999)] since we use tilted reconstruction slices instead of transaxial slices to approximate the spiral path. Theoretical considerations as well as the reconstruction of simulated phantom data in comparison to the gold standard 180 degrees LI (single-slice spiral CT) were carried out. Image artifacts, z-resolution as well as noise levels were evaluated for all simulated scanners. Even for a high number of detector rows the artifact level in the reconstructed images remains comparable to that of 180 degrees LI. Multiplanar reformations of the Defrise phantom show none of the typical cone-beam artifacts usually appearing when going to larger cone angles. Image noise as well as the shape of the respective slice sensitivity profiles are equivalent to the single-slice spiral reconstruction, z-resolution is slightly decreased. The ASSR has the potential to become a practical tool for medical spiral cone-beam CT. Its computational complexity lies in the order of standard single-slice CT and it allows to use available 2D backprojection hardware.

Planar G 2 transition between two circles with a fair cubic Bézier curve

Consumer products such as ping-pong paddles, can be designed by blending circles. To be visually pleasing it is desirable that the blend be curvature continuous without extraneous curvature extrema. Transition curves of gradually increasing or decreasing curvature between circles also play an important role in the design of highways and railways. Recently planar cubic and Pythagorean hodograph quintic spiral segments were developed and it was demonstrated how these segments can be composed pairwise to form transition curves that are suitable for G 2 blending. It is now shown that a single cubic curve can be used for blending or as a transition curve with the guarantee of curvature continuity and fairness. Use of a single curve rather than two segments has the benefit that designers and implementers have fewer entities to be concerned with.

Spirals and Rosettes in Architectural Ornament

Well-noted in nature for both its frequent appearance and its many variations, the spiral has inspired architectural forms for many centuries. The logarithmic spiral was adapted by the Greeks for the Ionic volute; many generations of architects developed geometrical constructions to approximate the curves of the spiral. A development on the theme of the spiral is the fan pattern, in which spiral segments are translated about the center of a circle. The superimposition of opposing fan patterns results in the rosette. The easily-constructed circular rosette is an ancient and beautiful pavement pattern, and can be varied to lay the base for many other motives.

Planar G2 curve design with spiral segments

Spiral segments are useful in the design of fair curves. Recent work demonstrated the composition of G 2 curves from planar cubic and Pythagorean hodograph quintic spiral segments. Practical cases that arise in the use of such spiral segments for computer-aided design are now explored. This paper describes an extension to additional cases of the technique for drawing with Bézier spiral segments that match the position, tangent and curvature of the end of another segment, to additional cases. The advantage of this technique is its control of the curvature and inflection points of a designed curve. The benefit of using such curves in the design of surfaces, in particular surfaces of revolution and swept surfaces, is the control of unwanted flat spots and undulations.

G2 curves composed of planar cubic and Pythagorean hodograph quintic spirals

Spiral segments are useful in the design of fair curves. They are important in CAD/CAM applications, the design of highway and railway routes, trajectories of mobile robots and other similar applications. A Pythagorean hodograph curve has the properties that its arc-length is a polynomial of its parameter, and the formula for its offset is a rational algebraic expression. Recent work demonstrated the composition of G 2 curves by joining circular arcs and/or straight line segments with cubic Bézier spiral segments and Pythagorean hodograph quintic spiral segments. These spiral segments are members of wider classes of spiral segments which are now examined. Selecting members from these wider classes of spiral segments allows for more flexible curve design; it is not necessary to incorporate circular arcs and straight line segments when using them.

Optimal circular arc interpolation for NC tool path generation in curve contour manufacturing

Circular arc interpolation is essential in manufacturing of curve contours. However, the problems of how to determine the parameters of the circular arcs and how to minimize the number of arcs according to desired interpolation accuracy have not been completely solved. This paper presents a new algorithm of circular arc interpolation for planar curves. It is based on the principle of minimax approximation. The algorithm has three features which include: (1) the interpolation error is minimax in any spiral segment of the curve, tangent-continuous at the joints of two spiral segments and satisfies the desired accuracy; (2) the parameters of the circular arcs depend on the desired accuracy and the number of arcs is fewest; (3) the circular arcs are compatible with the curve in concavity and convexity, and have almost the same radius of curvature, in other words, the interpolation looks very smooth and natural. Experimental trials show the algorithm is simple and robust for the application to NC contour manufacturing. The trials are carried out on producing the contour of a planar cam and a quadratic NURBS curve.