Axis Distance Research Articles

Nuclear magnetic relaxation of methyl protons in a paramagnetic protein: cross-correlation effects

Multi-exponential relaxation and concomitant relaxation allowed multiple quantum coherence among methyl protons in paramagnetic proteins arising from cross-correlation between Curie spin relaxation (CSR) and dipolar relaxation (DD) are investigated. Numerical simulations and semi-quantitative multi-quantum experiments in the cyanide-inhibited paramagnetic protein horseradish peroxidase underscore the presence of CSR×DD cross-terms. The magnitude of the resulting two-spin order depends on the distance and relative orientation of the methyl axis to the paramagnetic centre which can be exploited to derive structural constraints.

Bending Behavior of Woven Fabrics with Vertical Seams

This paper presents a study of the bending properties of fabric strips with vertical plain seam. The "second moment of area" of a seamed cross section determines the bending behavior of such a strip. Fabric thickness, seam thickness, distance of the neutral axis from the surface of the cross section, and seam allowance width are involved. Various woven fabrics with different seam allowances are investigated. Bending length and bending rigidity obtained from the experimental results are highly related to the second moment of area of the seamed fabric cross section.

Boundary Effects on Diffusiophoresis of Cylindrical Particles in Nonelectrolyte Gradients

The diffusiophoretic motion of a long circular cylinder in a transversely imposed gradient of a nonionic solute near a large plane wall parallel to its axis is analyzed. The range of the interaction between the solute and the solid surfaces is assumed to be small relative to the particle radius and to the gap width between the particle and the wall, but the polarization effect of the mobile solute in the thin diffuse layers adjacent to the solid surfaces caused by the strong adsorption of the solute is incorporated. A normal flux of the solute and a slip velocity of the fluid at the outer edge of the diffuse layers are used as the boundary conditions for the fluid domain outside the diffuse layers. Through the use of cylindrical bipolar coordinates along with these boundary conditions, a set of transport equations governing this problem is solved in the quasisteady situation and the wall effects on the diffusiophoresis of the cylinder are computed for various cases. For the diffusiophoretic motion of a cylinder normal to a plane, the particle mobility decreases monotonically with the decrease of the distance of the particle axis from the wall. The stronger the polarization effect in the diffuse layer, the weaker the wall effect on the diffusiophoresis. The effect of the normal plane on the diffusiophoresis of a cylinder is much more significant than that for a sphere at the same separation. For the diffusiophoresis of a cylinder parallel to a plane, the boundary effect is a complicated function of the relevant parameters (not necessarily varies monotonically with the extent of separation) mainly due to the existence of a diffusio-osmotic flow caused by the tangential fluid velocity at the plane wall.

ESEEM study of the location of spin-polarized chlorophyll-quinone radical pair in membrane-oriented spinach photosystems I and II complexes

Light-induced spin-polarized radical pairs, P700+A1 − in spinach photosystem (PS) I particles and P680+QA − in Zn-substituted PS II core complexes, in oriented membranes were studied by pulsed electron paramagnetic resonance (EPR). Based on the determined distance of 25.2 ± 0.2 A between P700 and A1, the angular dependence of the spin-polarized electron spin echo envelope modulation (ESEEM) spectra on the magnetic field suggests that the angle between $$R_{P700 - {\rm A}_1 } $$ , the radius-vector connecting P700 and A1, and the membrane normaln was 24 ± 4° in PS I particles. Obtained angle and distance of P700-A1 axis suggested QK side in the molecular geometry of cofactors presented in a recent X-ray crystallography of cyanobacterial PS I reaction center to be an active branch of electron transfer. The distance between P680 and QA was determined to be 27.4 ± 0.3 A for a nonoriented PS II. The angle between $$R_{P680 - Q_{\rm A} } $$ , the radius-vector connecting P680 and QA, andn was determined to be 21 ± 5°. The angle of P680-QA axis was close to that of 20° of P870-QA axis reported in X-ray analysis of the purple bacterial reaction center crystal.

Beam characteristics and clinical possibilities of a new compact treatment unit design combining narrow pencil beam scanning and segmental multileaf collimation

Not until the last decade has flexible intensity modulated three-dimensional dose delivery techniques with photon beams become a clinical reality, first in the form of heavy metal transmission blocks and other beam compensators, then in dynamic and segmented multileaf collimation, and most recently by scanning high-energy narrow electron and photon beams. The merits of various treatment unit and bremsstrahlung target designs for high-energy photon therapy are investigated theoretically for two clinically relevant target sites, a cervix and a larynx cancer both in late stages. With an optimized bremsstrahlung target it is possible to generate photon beams with a half-width of about 3 cm at a source to axis distance (SAD) of 100 cm and an initial electron energy of 50 MeV. By making a more compact treatment head and shortening the SAD, it is possible to reduce the half-width even further to about 2 cm at a SAD of 70 cm and still have sufficient clearance between the collimator head and the patient. One advantage of a reduced SAD is that the divergence of the beam for a given field size on the patient is increased, and thus the exit dose is lowered by as much as 1%/cm of the patient cross section. A second advantage of a reduced SAD is that the electron beam on the patient surface will be only about 8 mm wide and very suitable for precision spot beam scanning. It may also be possible to reduce the beamwidth further by increasing the electron energy up to about 60 MeV to get a photon beam of around 15 mm half-width and an electron beam as narrow as 5 mm. The compact machine will be more efficient and easy to work with, due to the small gantry and the reduced isocentric height. For a given target volume and optimally selected static multileaf collimator, it is no surprise that the narrowest possible scanned elementary bremsstrahlung beam generates the best possible treatment outcome. In fact, by delivering a few static field segments with individually optimized scan patterns, it is possible to combine the advantage of being able to fine tune the fluence distribution by the scanning system with the steeper dose gradients that can be delivered by a few static multileaf collimator segments. It is demonstrated that in most cases a few collimator segments are sufficient and often a single segment per beam portal may suffice when narrow scanned photon beams are employed, and they can be delivered sequentially with a negligible time delay. A further advantage is the increase of therapeutically useful photons and improved patient protection, since the pencil beam is only scanned where the leaf collimator is open. Consequently, some of the problems associated with dynamic multileaf collimation such as the tongue and groove and edge leakage effects are significantly reduced. Fast scanning beam techniques combined with good treatment verification systems allow interesting future possibilities to counteract patient and internal organ motions in real time.

Laminar natural convection from constant heat flux helical coiled tubes

An experimental investigation of a steady state natural convection from uniformly heated helical coiled tubes oriented horizontally in air has been made. Average heat transfer coefficients are obtained for laminar natural convection. The experiments have been carried out for four coils and for various values of heat fluxes of 500–5000 W m −2. The data are correlated with Rayleigh number using the coil tube diameter as the characteristic length. It is obtained that average heat transfer coefficient decreases with increasing the number of coil turns up to (or close to) the middle turn then a transition to turbulent begins. Correlation for all heat fluxes for all coils using the horizontal coil axis distance as a characteristics length is also presented.

レーザによる火炎中のOHおよびすす濃度の測定

This work was concerned at the oxidation of soot. An experimental study was made of two-dimensional visualization on soot particles and OH in diffussion/premixed flames by laser sheet. The soot volume fractions were obtained from the scattered light intensity of the soot by LLS (Laser-Light Scattered) method. OH distribution was measured by Planar Laser-induced Fluorescence (LIF) method. Quantitative laser measurements of OH in the zone of soot oxidation was made difficult by the presence of soot particles, which induced partial extinction and elastic scattering of the laser radiation. To improve the accuracy of the OH fluorescence signal, the spiked noises were reduced by the average of 25 shots measurements.Along the flame' s axis and radial distance, profiles of OH and soot concentrations were obtained over the zone where soot oxidation took place. The peak of the soot concentration was located just inside the position of the OH concentration peak (flame front), which indicated that soot was produced in the fuel rich region near the peak of the OH concentration. When the OH concentration was raised, the soot burnout rate increased.

Correcting kernel tilting and hardening in convolution/superposition dose calculations for clinical divergent and polychromatic photon beams

To account for clinical divergent and polychromatic photon beams, we have developed kernel tilting and kernel hardening correction methods for convolution dose calculation algorithms. The new correction methods were validated by Monte Carlo simulation. The accuracy and computation time of the our kernel tilting and kernel hardening correction methods were also compared to the existing approaches including terma divergence correction, dose divergence correction methods, and the effective mean kernel method with no kernel hardening correction. Treatment fields of 10 x 10-40 x 40 cm2 (field size at source to axis distance (SAD)) with source to source distances (SSDs) of 60, 80, and 100 cm, and photon energies of 6, 10, and 18 MV have been studied. Our results showed that based on the relative dose errors at a depth of 15 cm along the central axis, the terma divergence correction may be used for fields smaller than 10 x 10 cm2 with a SSD larger than 80 cm; the dose divergence correction with an additional kernel hardening correction can reduce dose error and may be more applicable than the terma divergence correction. For both these methods, the dose error increased linearly with the depth in the phantom; the 90% isodose lines at the depth of 15 cm were shifted by about 2%-5% of the field width due to significant underestimation of the penumbra dose. The kernel hardening effect was less prominent than the kernel tilting effect for clinical photon beams. The dose error by using nonhardening corrected kernel is less than 2.0% at a depth of 15 cm along the central axis, yet it increased with a smaller field size and lower photon energy. The kernel hardening correction could be more important to compute dose in the fields with beam modifiers such as wedges when beam hardening is more significant. The kernel tilting correction and kernel hardening correction increased computation time by about 3 times, and 0.5-1 times, respectively. This can be justified by more accurate dose calculations for the majority of clinical treatments.

The human horizontal vestibulo-ocular reflex during combined linear and angular acceleration.

We employed binocular magnetic search coils to study the vestibulo-ocular reflex (VOR) and visually enhanced vestibulo-ocular reflex (VVOR) of 15 human subjects undergoing passive, whole-body rotations about a vertical (yaw) axis delivered as a series of pseudorandom transients and sinusoidal oscillations at frequencies from 0.8 to 2.0 Hz. Rotations were about a series of five axes ranging from 20 cm posterior to the eyes to 10 cm anterior to the eyes. Subjects were asked to regard visible or remembered targets 10 cm, 25 cm, and 600 cm distant from the right eye. During sinusoidal rotations, the gain and phase of the VOR and VVOR were found to be highly dependent on target distance and eccentricity of the rotational axis. For axes midway between or anterior to the eyes, sinusoidal gain decreased progressively with increasing target proximity, while, for axes posterior to the otolith organs, gain increased progressively with target proximity. These effects were large and highly significant. When targets were remote, rotational axis eccentricity nevertheless had a small but significant effect on sinusoidal gain. For sinusoidal rotational axes midway between or anterior to the eyes, a phase lead was present that increased with rotational frequency, while for axes posterior to the otolith organs phase lag increased with rotational frequency. Transient trials were analyzed during the first 25 ms and from 25 to 80 ms after the onset of the head rotation. During the initial 25 ms of transient head rotations, VOR and VVOR gains were not significantly influenced by rotational eccentricity or target distance. Later in the transient responses, 25-80 ms from movement onset, both target distance and eccentricity significantly influenced gain in a manner similar to the behavior during sinusoidal rotation. Vergence angle generally remained near the theoretically ideal value during illuminated test conditions (VVOR), while in darkness vergence often varied modestly from the ideal value. Regression analysis of instantaneous VOR gain as a function of vergence demonstrated only a weak correlation, indicating that instantaneous gain is not likely to be directly dependent on vergence. A model was proposed in which linear acceleration as sensed by the otoliths is scaled by target distance and summed with angular acceleration as sensed by the semicircular canals to control eye movements. The model was fit to the sinusoidal VOR data collected in darkness and was found to describe the major trends observed in the data. The results of the model suggest that a linear interaction exists between the canal and otolithic inputs to the VOR.

Anisotropies in the Distribution of Satellite Galaxies

We find that satellites of isolated disk galaxies at projected radii between 300 and 500 kpc are distributed asymmetrically about the parent galaxy and aligned preferentially with the disk minor axis. The dynamical timescale at these radii is sufficiently long that the shape of this distribution must reflect the formation history of the outer halo rather than its internal evolution. We also find that the orbital angular momenta of satellites at projected major axis distances of 200 kpc tend to align with that of the central disk. These results demonstrate that satellites are dynamically related to their primary galaxy. Satellites drawn from current simulations of hierarchical galaxy formation exhibit neither the systematic alignment nor the net rotation with the central disk that we find in the data.

Dosimetric evaluation of the conformation of the multileaf collimator to irregularly shaped fields

The goal of this study was to evaluate the dosimetric characteristics of geometric MLC prescription strategies and compare them to those of conventional shielding block. Circular fields, square fields, and 12 irregular fields for patients with cancer of the head and neck, lung, and pelvis were included in this study. All fields were shaped using the MLC and conventional blocks. A geometric criterion was defined as the amount of area discrepancy between the MLC and the prescription outline. The "least area discrepancy" (LAD) of the MLC conformation was searched by selecting the collimator angle, meanwhile keeping a preselected position along the width of the leaf into the prescribed field. Five LAD conventions were studied. These included the LAD-0, LAD-1/3, LAD-1/2, and LAD-2/3 that inserted the leaves at the 0, 1/3, 1/2, and 2/3 of the leaf end into the prescription field, respectively. In addition, the LAD optimization was applied to the transecting (TRN) approach for leaf conformation that prescribed an equal area of overblocking and underblocking under each leaf. Film dosimetry was performed in a 20 cm polystyrene phantom at 10 cm depth 100 cm from source to axis distance (SAD) for both 6 and 18 MV photons with each of the above MLC conformations and conventional blocks. The field penumbra width, defined as the mean of the separation between the 20% and 80% isodose lines along the normal of the prescription field edge, was calculated using both the MLC and conventional block film dosimetry and compared. In a similar way, the d20 is defined as the mean separation between the 20% isodose line and the prescription field edge, and the d80 is defined as the mean separation between the 80% isodose line and the prescription field edge. The field penumbra width for all MLC conventions was approximately 2 mm larger than that of the conventional block. However, there was a larger variation of the separation distribution in the penumbra region of the irregular fields for the MLC, which had a standard deviation of 1 mm (a factor of 5 larger than the conventional block). The dosimetry for the circular fields showed that the LAD-TRN, LAD-1/2, and LAD-1/3 approximated the conventional blocking well in terms of d20 and d80; however, no single convention produced the best conformation for both measures. The dosimetric result of the patient treatment fields was similar for all sites. The LAD-1/3, LAD-1/2, and LAD-TRN strategies conformed to within 1 to 1.5 mm of the d80 of the conventional block for both 6 MV and 18 MV, respectively. The LAD-1/2 and LAD-TRN conformations were virtually identical, although it is proven analytically that the LAD-1/2 convention has the least overall area discrepancy of all conventions. The five MLC conformation conventions resulted in similar dosimetric penumbrae for all field shapes studied. The LAD-1/3, LAD-TRN, and LAD-1/2 produced the more favorable approximation to conventional block. The field penumbra width, although useful for evaluating irregular field shapes, could not describe the large local variations in the penumbra along the field edge for the MLC. These local variations could be of clinical concern when they appear near vital organs. However, the variation in a local region can potentially be reduced by minimizing the jaggedness of the leaf steps in that local region. The dosimetric results were useful as guidelines for the clinicians in the evaluation and adjustment of MLC leaf positions.

A new isocenter shift method for ideal geometric matching of two adjacent fields

The most commonly used technique for matching two adjoining parallel opposed fields has been geometric matching with a skin gap calculation. Many modifications have been suggested in order to minimize the shortcomings of this technique. Most of these, however, are more complex and time consuming in clinical practice, with little dosimetric improvement. We propose a simple new method for adjacent field abutment that climinates hot and cold spots due to different beam divergences. This method is based upon the use of a single match plane for both the cephalad and caudad parallel opposed beams. The divergence angle of these opposed beams is forced to be equal at the junction through the use of the same field length and the same target axis distance (TAD). For the isocentric treatment case, the procedure is summarized as follows. After setting up the cephalad AP PA fields to midplane in the conventional manner, the patient support couch is shifted longitudinally in the cephalad direction by a precise distance equal to the cephalad field length. The superior collimator of the caudad field is kept the same as for the cephalad field to ensure equal divergence angles. The actual irradiated volume of the caudad field is adjusted as needed by a large block or an asymmetric jaw. An analogous procedure is described for the nonisocentric case. This new isocenter shift method culminates in several distinct advantages over the other geometric methods. It provides the best homogeneous physical dose distribution in the junctional area (film dosimetry shows no hot or cold spots); it saves substantial time and efforts of dosimetricsts and reduces simulation time since there is no need to do gap calculations (sloping surface and difference in patient separation do not affect the results); and it can be easily verified by radiographic techniques using either skin wires or vertebral bodies as a guide. The isocenter shift method is more accurate and easier to set up than previously reported techniques, with marked dosimetric improvement. Where asymmetric jaws are available, this method should be considered as standard practice.

Effect of film-object distance on posteroanterior cephalometric measurements: Suggestions for standardized cephalometric methods

Posteroanterior (PA) cephalographs are used for diagnosis of transverse skeletal and dentoalveolar relationships. Unlike lateral head films, the variability of the PA radiograph has not been assessed. The purpose of this study was to evaluate the effect of film-object distance(film-ear rod, or film-porionic axis distance: FPD) and head angulation on transverse measurements from PA cephalographs. Seventeen skulls were selected from a total of 45 on the basis of strict criteria, including a stable reproducible centric occlusion. Radiographs were taken of each skull at the FPD of 11, 12, 13, and 14 cm. At the FPD of 11 and 14 cm, additional radiographs were taken at the angulations of +5° and −5° from the Frankfort horizontal (FH). Distances between the following landmarks were measured on the radiographs with digital calipers accurate to 0.01 mm: J (on the lateral contour of the maxilla), Ag (at the antegonial notch), Go (Gonion), Mb (buccal surface of mandibular first molar), IR (inner ramal point at the intersection of mandibular ramus and body). No clinically significant difference existed between measurements at the different FPDs evaluated. For this reason, and because the majority of PA films taken of 59 human subjects were within a FPD range below and including 13 cm, regression analyses were computed only at FPD = 13 cm. Correlation coefficients r between the distance AG-AG and distances J-J, IR-IR, and Mb-Mb were 0.71, 0.75, and 0.68, respectively. Transverse measurements were not significantly affected by a head angulation within 10° (FH −5° to +5°). Mean ratios between the maxillary distance J-J and the mandibular distances varied less than mean differences between maxillary and mandibular distances. The results of this study suggest that: (1) a film-porionic plane distance of 13 cm can be adopted as a standard for taking posteroanterior cephalographs, (2) in the evaluation of transverse relations between the jaws, ratios may be more accurate than absolute differences between maxillary and mandibular widths, (3) the landmarks commonly used to evaluate these widths (J and AG) seem appropriate, but their effectiveness in orthodontic diagnosis and treatment planning needs further investigation. (A M J O RTHOD D ENTOFAC O RTHOP 1995;108:30-7.)

The orbit of the double-line spectroscopic binary system HR 7112

We present velocity observations, obtained with the E. W. Fick Observatory 0.6 m telescope, of the 7th magnitudeK1 star HR 7112. Our observations show that HR 7112 is a double-line spectroscopic binary system composed of almost equal mass stars with a period of 215.6 days. The orbit has an eccentricitye = 0.142 and the stars orbit each other with a mean semi-major axis distance of approximately 0.4sin(i) AU. The masses of the stars are consistent with the classification as giant stars. Tidal effects are known to circularise the orbits of giant stars and this process is apparently underway in this system.

Li+ counterion self‐diffusion in ordered DNA

AbstractThe anisotropic self‐diffusion coefficient of 7Li+ (I = 3/2) counterions has been studied in hydrated, macroscopically oriented Li‐(B)DNA fibers at relatively high water contents, corresponding to approximate DNA‐DNA helix axis distances of 22–35 Å, using the pulsed field gradient hmr spin‐echo method. Self‐diffusion coefficients parallel (D∥) and perpendicular (D⟂) to the DNA helix axis increase with increasing salt content and with increasing DNA‐DNA helix axis distance. The observed anisotropy D∥/D⟂ decreases from 1.6 to 1.2 with the DNA‐DNA separation increasing from 22 to 35 Å in the salt‐free sample. This result can be understood by the obstruction effect caused by the DNA molecules themselves. The values of the Li+ self‐diffusion coefficients in the most water‐rich system with no added salt (corresponding to an approximate distance of 35 Å between the DNA helix axes) were D∥ ∼ 1.15 × 10−10 m2 s−1 and D⟂ ∼ 0.98 × 10−10 m2 s−1, compared to 9.14 × 10−10 m2 s−1 for the diffusion of Li+ in an aqueous solution of LiCl (∼ 2.1M). The possible occurrence of restriction effects in the DNA fibers have also been studied by determining the self‐diffusion coefficient at different effective diffusion times. The self‐diffusion coefficient of Li+ in the sample with the largest DNA‐DNA helix axis distance seems to be independent of the effective diffusion time, which indicates that the lithium ions are not trapped within impermeable barriers. The possibility of diffusion through permeable barriers has also been investigated, and is discussed. © 1994 John Wiley & Sons, Inc.

Dosimetry for asymmetric x-ray fields.

Conventional linear accelerators have four field-defining jaws or collimators. Usually, one set of the two opposing jaws moves concurrently to define the field width and the other set defines the field length. The resultant square or rectangular field will have the field centerline coincide with the collimator axis. However, some modern linacs have independent collimators or jaws that can be set asymmetrically. In this case, one of the two opposing jaws can be closed down independently of the other one to define an asymmetric field of smaller dimension. The field center now does not coincide with the collimator axis. Asymmetric collimators have found many clinical applications, but have complicated the dosimetry for physicists. Data acquisition and treatment planning implementations are tedious and complicated. An algorithm has been developed to correct for the reduced dose in the smaller asymmetric field. The approach used is similar in principle to the Day's equivalent field calculation. The difference in dose between an asymmetric and a symmetric radiation field is accounted for by a correction factor that is a function of the asymmetric and symmetric field sizes, off axis distance, and depth of measurement. The correction method presented here applies only to the closing down of one independent jaw. Beam profiles for asymmetric fields are measured for both the 6 and 10 MV photon beams.(ABSTRACT TRUNCATED AT 250 WORDS)

Relation between increase in length of hip axis in older women between 1950s and 1990s and increase in age specific rates of hip fracture.

To determine whether length of hip axis in elderly women has increased over the past 40 years and, if so, whether the increase may have contributed to the increase in the age adjusted rate of hip fractures during those years. Retrospective assessment of anteroposterior x ray films of the pelvis. Radiology department of a rheumatology hospital, New Zealand. Two cohorts of women aged > 60 (mean 70) who were x rayed on the same apparatus in either the 1950s or the 1990s. Length of hip axis (distance from the medial aspect of the pelvis to the lateral aspect of the femur along the axis of the femoral neck), length of femoral neck (length of hip axis excluding the femoral head and more medial structures), and width of femoral neck (see figure). Both the mean length of the hip axis and the mean length of the femoral neck were significantly greater in the women whose x ray films were taken in the 1990s than in those in the 1950s (124.0 mm (SE 1) v 130.5 (1), P = 0.0002; 79.4 (1) v 84.9 (1), P < 0.0001, respectively). The width of the femoral neck did not change, and the lengths expressed as ratios to width were greater in the more recent x ray films, indicating that these findings are not due to an unrecognised change in radiographic technique. An increase in the length of the hip axis in elderly women in New Zealand during the past 40 years has occurred which is large enough to account for the increase in the age adjusted rate of hip fractures during those years.

Landscape habitat diversity: a multiscale information theory approach

Abstract Biotic diversity is a topic of increasing concern, but current tools for quantifying diversity at the landscape level are inadequate. A new index is proposed. Beginning with a classified raster image of a landscape, each habitat type is assigned a value based on an ordination axis distance. The change in value from one location to the next depends on how similar the two locations are. An information measure d I is used to evaluate deviation from uniformity of the ordination values at different spatial scales. Different maps can be compared if habitat values are based on the same ordination scale. This new method provides a powerful tool for both displaying and calculating landscape habitat diversity.

On the activity and orbit of the Geminids meteorid stream

The activity of the Geminids meteor shower is studied on the basis of radio observations carried out by the Budrio meteor radar in 1986. The 1986 Geminids have displayed as a distinct meteor shower with an asymmetric curve of activity, the duration between the points of one-quarter strength being 6 days and the maximum at the solar longitude of about 260°.75 (1950.0). The mean orbit and radiant ephemeris of the Geminids are derived on the basis of 191 precise photographic orbits available from the IAU Meteor Data Centre in Lund. Over a time span of 50 years, the semi-major axis, eccentricity and perihelion distance of the stream exhibit variations following the trend of the stream evolution suggested by Williams and Wu.

Conditions of crank existence for a particular case of the RSSR linkage

Necessary and sufficient conditions of motion transfer for a particular case of the RSSR linkage is further derived and simplified. This particular case is considered when the frame is coincided with input and output axes distance, which may also be called as “simply skewed form” of RSSR. The results show that the conditions of crank existence for this particular case can be represented in a way quite resembling the Grashof criterion applicable to planar four bar linkages, and thus are of very simple expression and geometric sense. (The term “simple” normally implies that overhand computation by “rigours” programming may not be needed.)