Mutual Collisions Research Articles

Accretion of tidally disrupted asteroids on to white dwarfs: direct accretion versus disc processing

ABSTRACT Atmospheric heavy elements have been observed in more than a quarter of white dwarfs (WDs) at different cooling ages, indicating ongoing accretion of asteroidal material, whilst only a few per cent of the WDs possess a dust disc, and all these WDs are accreting metals. Here, assuming that a rubble-pile asteroid is scattered inside a WD’s Roche lobe by a planet, we study its tidal disruption and the long-term evolution of the resulting fragments. We find that after a few pericentric passages, the asteroid is shredded into its constituent particles, forming a flat, thin ring. On a time-scale of Myr, tens of per cent of the particles are scattered on to the WD, and are therefore directly accreted without first passing through a circularized close-in disc. Fragment mutual collisions are most effective for coplanar fragments, and are thus only important in 103−104 yr before the orbital coplanarity is broken by the planet. We show that for a rubble pile asteroid with a size frequency distribution of the component particles following that of the near earth objects, it has to be roughly at least 10 km in radius such that enough fragments are generated and $\ge 10{{\ \rm per\ cent}}$ of its mass is lost to mutual collisions. At relative velocities of tens of km s−1, such collisions grind down the tidal fragments into smaller and smaller dust grains. The WD radiation forces may shrink those grains’ orbits, forming a dust disc. Tidal disruption of a monolithic asteroid creates large km-size fragments, and only parent bodies ≥100 km are able to generate enough fragments for mutual collisions to be significant. Hence, those large asteroids experience a disc phase before being accreted.

Ultrafast electron holes in plasma phase space dynamics

Electron holes (EH) are localized modes in plasma kinetic theory which appear as vortices in phase space. Earlier research on EH is based on the Schamel distribution function (df). A novel df is proposed here, generalizing the original Schamel df in a recursive manner. Nonlinear solutions obtained by kinetic simulations are presented, with velocities twice the electron thermal speed. Using 1D-1V kinetic simulations, their propagation characteristics are traced and their stability is established by studying their long-time evolution and their behavior through mutual collisions.

Ryugu\u2019s observed volatile loss did not arise from impact heating alone

Carbonaceous asteroids, including Ryugu and Bennu, which have been explored by the Hayabusa2 and OSIRIS-REx missions, were probably important carriers of volatiles to the inner Solar System. However, Ryugu has experienced significant volatile loss, possibly from hypervelocity impact heating. Here we present impact experiments at speeds comparable to those expected in the main asteroid belt (3.7 km s−1 and 5.8 km s−1) and with analogue target materials. We find that loss of volatiles from the target material due to impacts is not sufficient to account for the observed volatile depletion of Ryugu. We propose that mutual collisions in the main asteroid belt are unlikely to be solely responsible for the loss of volatiles from Ryugu or its parent body. Instead, we suggest that additional processes, for example associated with the diversity in mechanisms and timing of their formation, are necessary to account for the variable volatile contents of carbonaceous asteroids.

Early terrestrial planet formation by torque-driven convergent migration of planetary embryos

The massive cores of the giant planets are thought to have formed in a gas disk by the accretion of pebble-sized particles whose accretional cross-section was enhanced by aerodynamic gas drag1,2. A commonly held view is that the terrestrial planet system formed later (30–200 Myr after the dispersal of the gas disk) by giant collisions of tens of lunar- to Mars-sized protoplanets3,4. Here we propose, instead, that the terrestrial planets of the Solar System formed earlier by the gas-driven convergent migration of protoplanets towards ~1 au. To investigate situations in which convergent migration occurs and determine the thermal structure of the gas and pebble disks in the terrestrial planet zone, we developed a radiation–hydrodynamic model with realistic opacities5,6. We find that protoplanets grow in the first 10 Myr by mutual collisions and pebble accretion, and gain orbital eccentricities by gravitational scattering and the hot-trail effect7,8. The orbital structure of the inner Solar System is well reproduced in our simulations, including its tight mass concentration at 0.7–1 au and the small sizes of Mercury and Mars. The early-stage protosolar disk temperature exceeds 1,500 K inside 0.4 au, implying that Mercury grew in a highly reducing environment next to the evaporation lines of iron and silicates, influencing Mercury’s bulk composition9. A dissipating gas disk, however, is cold, and pebbles drifting from larger heliocentric distances would deliver volatile elements. A full 2D radiation–hydrodynamic model of a protoplanetary disk shows that rocky planets can be formed early, and not tens of million years after the dispersal of the gas disk as usually assumed, by means of gas-driven migration of planetesimals around 1 au. The model reproduces well the structure of the inner Solar System.

Dependencies of Mantle Shock Heating in Pairwise Accretion

Abstract The final assembly of planets involves mutual collisions of large similar-sized protoplanets (“giant impacts”), setting the stage for modern geologic and atmospheric processes. However, thermodynamic consequences of impacts in diverse (exo)planetary systems/models are poorly understood. Impact velocity in “self-stirred” systems is proportional to the mass of the colliding bodies (v imp ∝ M 1/3), providing a predictable transition to supersonic collisions in roughly Mars-sized bodies. In contrast, nearby larger planets, or migrating gas giants, stir impact velocities, producing supersonic collisions between smaller protoplanets and shifting outcomes to disruption and nonaccretion. Our particle hydrocode simulations suggest that thermodynamic processing can be enhanced in merging collisions more common to calmer dynamical systems due to post-impact processes that scale with the mass of the accreting remnant. Thus, impact heating can involve some contribution from energy scaling, a departure from pure velocity-scaling in cratering scenarios. Consequently, planetary thermal history depends intimately on the initial mass distribution assumptions and dynamical conditions of formation scenarios. In even the gentlest pairwise accretions, sufficiently large bodies feature debris fields dominated by melt and vapor. This likely plays a critical role in the observed diversity of exoplanet systems and certain debris disks. Furthermore, we suggest solar system formation models that involve self-stirred dynamics or only one to a few giant impacts between larger-than-Mars-sized bodies (e.g., “pebble accretion”) are more congruent with the “missing mantle problem” for the main belt, as we demonstrate debris would be predominantly vapor and thus less efficiently retained due to solar radiation pressure effects.

Numerical effectiveness investigation of the automatic ball balancer with a deep chamber

The article describes the simulation results of an unbalanced rotary machine with an automatic ball balancer with a deep chamber (ABB-DC) based on a mathematical model of such a system. The ABB chamber has a cylindrical shape and is filled with balls that can move freely in general motion. The model takes into account mutual collisions between the balls, as well as between the balls and the chamber. The model also includes friction forces and rolling resistance. The comparison of simulation results performed with two different construction types of the chamber, classic single-layer drum (ABB-SC) and ABB-DC, confirmed the better efficiency of the ABB-DC in the optimal range of the number of balls. The machine body movement was limited to planar motion. The correctness of such a limitation has been verified by analyzing waveforms of reaction forces of constraints and their moments. Waveforms were divided into transient and steady states. The results of the analysis indicate the additional constraints do not significantly affect machine body movements. However, this might affect the ball arranging process in the ABB chamber. The paper also presents details of performing numerical simulations based on the developed mathematical model and numerical tests to determine the optimal integration time-step.

A Supernova-driven, Magnetically Collimated Outflow as the Origin of the Galactic Center Radio Bubbles

Abstract A pair of nonthermal radio bubbles recently discovered in the inner few hundred parsecs of the Galactic center bears a close spatial association with elongated, thermal X-ray features called the X-ray chimneys. While their morphology, position, and orientation vividly point to an outflow from the Galactic center, the physical processes responsible for the outflow remain to be understood. We use 3D magnetohydrodynamic simulations to test the hypothesis that the radio bubbles/X-ray chimneys are the manifestation of an energetic outflow driven by multiple core-collapsed supernovae (SNe) in the nuclear stellar disk, where numerous massive stars are known to be present. Our simulations are run with different combinations of two main parameters, the supernova birth rate and the strength of a global magnetic field being vertically oriented with respect to the disk. The simulation results show that a hot gas outflow can naturally form and acquire a vertically elongated shape due to collimation by the magnetic pressure. In particular, the simulation with an initial magnetic field strength of 80 μG and a supernova rate of 1 kyr−1 can well reproduce the observed morphology, internal energy, and X-ray luminosity of the bubbles after an evolutionary time of 330 kyr. On the other hand, a magnetic field strength of 200 μG gives rise to an overly elongated outflow that is inconsistent with the observed bubbles. The simulations also reveal that, inside the bubbles, mutual collisions between the shock waves of individual SNe produce dense filaments of locally amplified magnetic field. Such filaments may account for a fraction of the synchrotron-emitting radio filaments known to exist in the Galactic center.

The radial structure of planetary bodies formed by the streaming instability

Comets and small planetesimals are believed to contain primordial building blocks in the form of millimeter to centimeter sized pebbles. One of the viable growing mechanisms to form these small bodies is through the streaming instability (SI) in which pebbles cluster and gravitationally collapse toward a planetesimal or comet in the presence of gas drag. However, most SI simulations are global and lack the resolution to follow the final collapse stage of a pebble cloud within its Hill radius. We aim to track the collapse of a gravitationally bound pebble cloud subject to mutual collisions and gas drag with the representative particle approach. We determine the radial pebble size distribution of the collapsed core and the impact of mutual pebble collisions on the pebble size distribution. We find that virial equilibrium is never reached during the cloud evolution and that, in general, pebbles with a given Stokes number (St) collapse toward an optically thick core in a sequence from aerodynamically largest (St ~ 0.1) to aerodynamically smallest (St ~ 2 × 10−3). We show that at the location where the core becomes optically thick, the terminal velocity vt,* ~ 60 m s−1St2 is well below the fragmentation threshold velocity. While collisional processing is negligible during cloud evolution, the collisions that do occur are sticking. These results support the observations that comets and small planetary bodies are composed of primordial pebbles in the millimeter to centimeter size range.

Multi-UAV trajectory planning using gradient-based sequence minimal optimization

Multi-UAV system is widely used in surveillance, search and rescue, and industrial inspection. Multi-UAV trajectory planning is crucial for the multi-UAV system, but multi-UAV trajectory planning often needs to consider many constraints, such as trajectory smoothness, obstacle collisions, mutual collisions, dynamic limits, time-consuming, and trajectory length. It is a challenge to balance these constraints while considering computational performance. This paper proposes a novel multi-UAV trajectory planning method to solve the challenge. This method uses time segmentation instead of traditional waypoint segmentation to establish a trajectory optimization model based on the unified time interval, which simplifies the calculation of cost functions. At the same time, virtual segments are introduced to adapt to the trajectory length of different UAVs to reduce the total arrival time. Nonlinear constraints are cast into cost functions and a gradient-based sequential minimal optimization (GB-SMO) algorithm is proposed to minimize the cost function, which decouples the constraint of the mutual collisions in each iteration to save the planning time. Experiments are performed on a multi-UAV system to prove the effectiveness of the proposed method. Results show that this method has good performance in obstacle-rich environments and is efficient for a large number of UAVs.

Determination of the Energy of a Primary Particle in Accordance with the Hypothesis of Primary Particles and Another Meaning of Planck Mass

This paper represents a continuation of our Hypothesis of primary particles, which provides an opportunity for describing the origin of the Big Bang and other universes. In its hypothesis, we have shown that there was a possibility of hypothetical primary particles moving in their own flat spacetime, in their basic, dynamic state and possessing speeds much higher than the speed of light, acquiring energy and momentum during deceleration in mutual collisions, which would tunnel into various universes. The cosmic microwave background is evidence that our universe expanded from a very hot, dense state, which is consistent with our hypothesis. The lower border speed to which a primary particle at the Big Bang came very close in a collision during its deceleration, simultaneously represents the upper border speed in our Universe—the speed of light in a vacuum. The speed of light, along with other fundamental physical constants, had shaped our Universe, in a manner in which we are still able to recognize the “physical gene” that preceded our existence. By virtue of comprehending our Universe, using the help of fundamental physical constants, we have determined that the mass attributed to the primary particle, in accordance with the Hypothesis of primary particles, would correspond to the Planck mass. Therefore, energy of the primary particle would be: Ep ≈ 1.22 × 1019 GeV.

The development of spallation target and fuel handling system for China initiative accelerator driven system

The China initiative Accelerator Driven subcritical System (CiADS) has already embarked on a plan to be built in south China’s Guangdong province for the research purpose of lead–bismuth cooled fast reactor and minor-actinide transmutation technology. In comparison with the other critical reactors, it is difficult to arrange the fuel handling equipment and to make the whole core refueling plan, since there is a proton beam tube in the central of the core and the operating environment is completely opaque. In this context, an innovation design of the spallation target and fuel handling system is proposed in Institute of Modern Physics, Chinese Academy of Sciences (IMPCAS) based on an immersive Virtual Reality (VR) platform, which can fulfill the loading and refueling procedure without mutual collisions, and provide the real-time roaming experience as in the real world. Detailed information of the handling system have been introduced including the optimized logical structure in consideration of the movement of spallation target for the fuel handling process, the principle of collision detection based on the fast ray-casting technology, the real-time roaming experience with feedback control in refueling procedure, and the reliability assessment and sequential optimization for the above process. The spallation target and fuel handling system can cover all the assemblies in subcritical reactor and provide a powerful tool for the frequently updated engineering design of the CiADS project.

Limits on Protoplanet Growth by Accretion of Small Solids

Abstract This paper identifies constraints on the growth of a small planetary core (0.3 M ⊕) that accretes millimeter-sized pebbles from a gaseous disk. We construct time-dependent spherical envelope models that capture physical processes that are not included in existing global hydrodynamic simulations, including particle size evolution, dust transport, and realistic gas equations of state. We assume a low enough disk density that pebbles are marginally coupled to the gas and are trapped efficiently near the core Bondi radius. Pebbles then drift rapidly enough to experience erosion by sandblasting, mutual collisions, and sublimation of water ice. We find that pebble fragmentation is more efficient than dust resticking. Therefore the high pebble accretion rate needed to build a core of mass >M ⊕ leads to a high envelope metallicity and grain opacity. Above yr−1, and without other luminosity sources, convective motions expand near the Bondi radius. The warm, dusty, and turbulent envelope buffers the inward drift of pebble debris: given a turbulent concentration factor f turb ≳ 1 near the lower convective boundary, the core growth rate is limited to 1 × 10−7 f turb M ⊕ yr−1 and the e-folding time 3/f turb Myr. The remainder of the solid debris is expelled as highly processed silicates. Pebble ice never reaches the core, and the envelope contains comparable amounts of H2/He and metals. We interpret our results using simpler steady models and semianalytical estimates. Future global simulations incorporating the processes modeled here are needed to understand the influence of rotation and vertical disk structure.

Kinetics of cluster formation in active suspension: Coarsening regime.

The active suspension has an amazing property to undergo a phase transition into dense and dilute gas phases, even in the absence of the interparticle forces of attraction. In this work, the phase transition in active suspension is considered within a minimal model, in which self-propelled particles are moving with a constant speed, while their direction of propagation is governed by mutual collisions. The final stage of cluster formation in active suspension is studied when the larger clusters grow by consuming the smaller ones. The analysis of kinetic equation for the evolution of the number of particles in a cluster and conservation of particles law in active suspension shows that the number of clusters decreases with time according to a power of minus three fifths and the average number of particles in a cluster depends on their speed and time in the power of three fifths. The size distribution function of clusters is obtained, which is found to be asymmetric with respect to the average number of particles in clusters.

The tensile strength of compressed dust samples and the catastrophic disruption threshold of pre-planetary matter

ABSTRACT During the planetary formation process, mutual collisions among planetesimals take place, impacting on their porosities. The outcome of these collisions depends, among other parameters, on the tensile strength of the colliding objects. In the first stage of this work, we performed impact experiments into dust samples, assembled with material analogous to that of the primitive Solar System, to obtain highly compressed samples that represent the porosities measured in chondritic meteorites. In the second stage, we obtained the tensile strengths of the compressed dust samples by the Brazilian Disc Test. We found a correlation between the tensile strength and the volume filling factor of the compressed dust samples and obtained the corresponding critical fragmentation strength in mutual collisions and its dependence on the volume filling factor. Finally, we give prescriptions for the catastrophic disruption threshold as a function of the object size, for different values of the volume filling factor.

Evaporative loss of moderately volatile metals from the superheated 1849 Ma Sudbury impact melt sheet inferred from stable Zn isotopes

The retention of moderately volatile elements on the growing Earth remains a major uncertainty in models of terrestrial accretion. Large impactors were the main carriers of accreted material but their mutual energetic collisions and impacts onto the Earth also caused chemical fractionation for which limited experimental data exist. The objective of this work was to study several moderately volatile elements in the third-largest impact basin preserved on Earth at Sudbury, Ontario. We conducted a new chemostratigraphic transect (n=41) of Zn isotope ratios and concentrations by analysing melt sheet and basin fill samples. The data were compared to common Pb, Cs, Cd and Sb concentration systematics. Within the crystallised melt sheet there are strong trends in the extent of moderately volatile element deficits, Zn isotope composition (δ66/64ZnJMC-L from 0.18 to 0.47‰) and initial Pb isotope composition. The combined evidence suggests that these trends reflect footwall contamination of a melt sheet that had experienced evaporative Zn-loss of up to 75–80%. Accounting for plausible isotopic signatures of target rocks, the maximum mass-dependent Zn isotope fractionation ε was 0.29 ± 0.04‰ (1 s.d.), which translates to modest fractionation factors α=0.99986 to 0.99975. This is comparable to melt fallout-glass and fused sands from nuclear detonation sites. We attribute the observed Zn loss and isotope fractionation to the formation of the impact melt. The rapid formation of a solid lid of breccias upon seawater ingress may have prevented stronger evaporative loss and isotope fractionation. Within the crater fill, there is an up-stratigraphy increase in Zn isotope variability (δ66/64ZnJMC-L from 0.29 to 1.05‰). Combined with evidence for biogenic reduced C, this suggests sedimentation of authigenic particulates within an enclosed crater sea.In the melt sheet, the Zn-Pb and Rb-Cs pairs experienced different extents of maximum evaporative loss (Pb up to 98.4% vs. Zn 78%; and Cs ∼90% vs. Rb ∼30%). The relative loss pattern could reflect evaporation from superheated silicate melt at ∼1,450°C and 1 atm. Loss from super-liquidus melts formed by bolide impacts could have been a significant process shaping the Earth's volatile and moderately volatile inventory.

Effect of Imposed Shear Strain on Steel Ring Surfaces during Milling in High-Speed Disintegrator.

This contribution characterizes the performance of a DESI 11 high-speed disintegrator working on the principle of a pin mill with two opposite counter-rotating rotors. As the ground material, batches of Portland cement featuring 6–7 Mohs scale hardness and containing relatively hard and abrasive compounds with the specific surface areas ranging from 200 to 500 m2/kg, with the step of 50 m2/kg, were used. The character of the ground particles was assessed via scanning electron microscopy and measurement of the absolute/relative increase in their specific surface areas. Detailed characterization of the rotors was performed via recording the thermal imprints, evaluating their wear by 3D optical microscopy, and measuring rotor weight loss after the grinding of constant amounts of cement. The results showed that coarse particles are ground by impacting the front faces of the pins, while finer particles are primarily milled via mutual collisions. Therefore, the coarse particles cause higher abrasion and wear on the rotor pins; after the milling of 20 kg of the 200 m2/kg cement sample, the wear of the rotor reached up to 5% of its original mass and the pins were severely damaged.

Escape of rock-forming volatile elements and noble gases from planetary embryos

Large planetesimals and planetary embryos ranging from several hundred to a few thousand kilometers can develop magma oceans through mutual collisions, gravitational energy, and the heating of short-lived radioactive elements. During their solidification after the dissipation of the disk a steam atmosphere will be catastrophically outgassed and may be lost efficiently via hydrodynamic escape, as long as it does not condense. The escaping H-atoms that originate from the dissociation of H2O and H2 will drag heavier trace elements like noble gases such as Ne and Ar and outgassed moderately volatile rock-forming elements such as K, Na, Si, Mg, etc. into space. Under consideration of various EUV flux evolution scenarios of young solar-type stars, we apply an upper atmosphere hydrodynamic escape model that includes the dragging of heavier species by escaping H-atoms. We investigate the atmospheric/elemental escape and fractionation from planetary embryos with masses of 1 MMoon, 0.5 MMars, 1 MMars, and 1.5 MMars at different orbital distances between the orbits of Venus and Mars. Our results indicate that the steam atmospheres and the embedded trace elements will be lost efficiently before they condense for masses ≤0.5 MMars and orbital distances up to 1 AU. For heavier embryos of up to 1.5 MMars almost all of the considered steam atmospheres can be lost within ≈12 Myr, which lies within the time frame of the formation of the first Martian protocrust after ≈20 Myr, i.e. for such steam atmospheres to be lost completely a shallow magma ocean must remain below the atmosphere, which might be achieved through frequent impacts onto the planetary embryo. The considered outgassed noble gases and rock-forming elements will be completely dragged away together with the steam atmospheres under the assumption that the trace elements will reach the thermosphere. For embryos with masses ≤MMoon the gravity is too weak for a dense atmosphere to build up for the high magma ocean related surface temperatures and all outgassed elements will escape immediately to space. For all considered planetary masses and orbits the loss rates of Ar and Ne are so high that there will be no fractionation of their isotopes. The studied planetary embryos, even though not isotopically fractionated, will therefore be severely depleted in noble gases and moderately volatile elements. Hydrodynamic escape might then also affect the final composition of terrestrial planets that accrete out of such planetary embryos, such as the volatile content and the Fe/Mg ratio of a planet.

Migration of Giant Gaseous Clumps and Structure of the Outer Solar System

New data on the distribution of distant trans-Neptunian objects and on the properties of comets indicate the importance of dynamical processes in the outer part of the protoplanetary disk in the formation of the observed structure of the Solar system. In this paper, we examined the possible action of giant gaseous clumps, resulting from gravitational instability and fragmentation of circumstellar disks, on the orbital distribution of the population of small bodies in the outer Solar system. Basically, we studied those features of migration and gravitational interaction of giant clumps that were found previously by Vorobyov and Elbakyan (2018). Our modeling showed that the main features of the distribution of small bodies resulting from the gravitational influence of giant clumps are consistent with the observed orbital distribution of distant trans-Neptunian objects. The studied dynamical process associated with a single giant clump is very short-time event (no more than several tens of thousands of years). The main factor affecting the orbital distribution of small bodies is close encounters with giant clumps. A significant part of small bodies (comets) is very quickly transferred to distant orbits with large eccentricities, which allows them to avoid mutual collisions.

Crater-ray formation through mutual collisions of hypervelocity-impact induced ejecta particles

We investigate the patterns observed in ejecta curtain induced by hypervelocity impact (2–6 km/s) with a variety of the size and shape of target particles. We characterize the patterns by an angle, defined as the ratio of the characteristic length of the pattern obtained by Fourier transformation to the distance from the impact point. This angle is found to be almost the same as that obtained by the reanalysis of the patterns in the previous study at lower impact velocities (Kadono et al., 2015, Icarus 250, 215–221), which are consistent with lunar crater-ray systems. Assuming that the pattern is formed by mutual collision of particles with fluctuation velocity in excavation flow, we evaluate an angle at which the pattern growth stops and show that this angle is the same in the order of magnitude as the ratio of the fluctuation velocity and the radial velocity. This relation is confirmed in the results of experiments and numerical simulations. Finally, we discuss the dependence of the patterns on impact conditions. The experiments show no dependence of the angle on impact velocity. This indicates that the ratio between the fluctuation and radial velocity components in excavation flow does not depend on impact velocity. Moreover, the independences on particle size and particle shape suggest that the angle characterizing the structure of the patterns does not depend on cohesive force. Since cohesive forces should be related with elastic properties of particles, the structure does not depend on elastic properties, though inelastic collisions are important for the persistence and contrast of the patterns.

Design of a Modular Continuum-Articulated Laparoscopic Robotic Tool With Decoupled Kinematics

Robot-assisted laparoscopic minimally invasive surgery has gained significant attentions due to its enhanced dexterity, improved precision, natural eye-hand coordination, etc. In these procedures, stick-like surgical tools with distal wrists are usually maneuvered by multiple patient-side manipulators to perform an operation. These patient-side manipulators shall realize remote center of motion movements and are subject to risks of mutual collisions during motion. On the other hand, the continuum surgical manipulators, often with multiple segments, usually have several degrees of freedom (DoFs) for the movements in a patient's cavity, and only need a lockable bedside stand, rather than a manipulator. However, the continuum segments inherently have limited bending curvature such that large orientation changes of the surgical end effector around confined anatomical features can be challenging. This letter, hence, proposes a modular continuum-articulated laparoscopic robotic tool design with simple and decoupled kinematics. An inverted dual-continuum mechanism is used in the tool to realize pure translations, while a 2-DoF cable-driven distal wrist is incorporated for orientations. The utilized dual-continuum mechanism maintains a constant length across its entire cross section to significantly facilitate maintaining tensions for the actuation cables of the distal wrist. Design concept, kinematics, system descriptions, actuation calibration, and experimental characterizations are reported, demonstrating effectiveness of the proposed idea.