Ackermann Yönlendirme Geometrisi. Ackermann цемент


Ackermann Yönlendirme Geometrisi - Analizsimulasyon.com

Ackermann yönlendirme geometrisi, genel olarak tekerlek üzerinde statik olarak tanımlı olan toe  açısının dinamik olarak değişmesini sağlar.Yani diğer bir değişle ilgili geometriye sahip olan bir vasıtanın dış tekerleği x kadar dönüyorsa iç tekerleği y (y>x) kadar dönmektedir.Bu şekilde bir şeyin yapılmasının temel nedeni iç  ve dış tekerleğin dönüş sırasında farklı hızlarda olmasıdır.  Eğer bu geometri olmasaydı, yani iç ve dış tekerlekler  aynı açılarda dönüştürülseydi. İç tekerlek dönmesi gereken daire ile aynı yönde olamayacak ve iç tekerlek üzerinde daha çok slip meydana gelerek lastik daha çabuk aşınacaktır. Ayrıca iç tekerleğin  yer ile olan tutunması azalacaktır.

İç ve Dış Tekerleğin Farklı Yarı Çağlarda Dönmesi

Dönüş sırasında tekerleklerin birbirine göre farklı miktarlarda döndürülmesi , aralarında bazı açılar verilmiş olan geometrik yapılar ile gerçekleştirilmektedir.  Bununla ilgili formülleri teorik bilgiler önümüzdeki günlerde analizsimulasyon.com üzerinden paylaşılacaktır.

Ackermann Yönlendirme Açıları

Gerçek Ackerman Açısı

Gerçek ackerman açısı sağdaki resimde de görüldüğü üzere kingpin üzerinde bulunan tie rodların birbiri arasında açı verimesidir.  Bu açı belirlenirken tierodların kesişimleri arka aks

ın ortası olmasına dikkat edilir. Bu şekilde verilen bir  açı ile iç tekerlekte (sağda  görüldüğü gibi )hiç bir Toe açısı değişimi meydana gelmez ve izlemesi gereken daireyi izler.

Fazla verilen Ackerman Açısı

Eğer tie rodların uzantıları solda görüldüğü gibi arka aksın önünde kesişirse, fazladan ackerman açısı verilmiştir denilebilir. Bu şekilde bir ackerman açısı  verildiğinde iç

tekerlek izlemesi gereken daireden daha küçük bir daireyi izlemeye çalışır ve tekerlek üzerinde aracı döndürmeye yönelik daha fazla kuvvet oluşur.

Daha Az Verilen Ackerman Açısı

Araç tasarımı sırasında ackerman açısı ideal olandan daha az verilebilir. Böylelikle tie rodların kesişimleri arka aksın dahada  gerisinde gerçekleşir. Sağdaki resimde de görüldüğü gibi lastik bu şekilde verilmiş olan bir ackerman açısında izlemesi gereken daireden daha büyük bir daire izlemeye çalışır ve aracın dönüş kabiliyeti düşer. İç tekerlek üzeride toe in açısı oluşur.

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Ackerman Prensibi Nedir?

08.04.2016 tarihli yazı 17763 kez okunmuştur.

Bir direksiyon sisteminin özellikleri şu şekilde özetlenebilir;

► Yol yüzeyindeki bozukluklardan kaynaklanan sarsıntılar direksiyon simidine iletilirken mümkün olduğunca sönümlenmelidir. Ancak bu sönümleme sürücünün yol ile temas hissini kaybetmesine izin vermemelidir.► Temel direksiyon kinematiği tasarımı Ackerman koşulunu sağlamalıdır. Araç dönüş halinde iken sağ ve sol ön tekerlek eksen uzantıları, arka aks eksen uzantısı üzerinde aynı noktada kesişmelidir.► Direksiyon sisteminin katılığı (özellikle eğer elastik-plastik bağlantılar kullanılıyorsa) taşıtın küçük direksiyon düzeltmelerine reaksiyon göstermesini engellememelidir.► Direksiyon simidi bırakıldığında, tekerlekler kendiliğinden düz konuma dönmeli ve bu pozisyonda dengede kalmalıdır.► Kolay kullanım için mümkün olduğunca az direksiyon oranı olmalıdır. Böylece oluşan direksiyon kuvvetleri sadece direksiyon oranı ile değil ön aks yükü, dönüş dairesi boyutu, tekerlek süspansiyonu ve doğrultusu (kaster, kingpin açısı, direksiyon yuvarlanma dairesi yarıçapı) ve lastik profili ile belirlenir. 

Direksiyon sistemlerinin sağlaması gereken teknik şartlar vardır. S38StV20’ye (Federal Alman Motorlu Taşıt Emniyet standartları (FMVSS/CUR)) göre direksiyon sistemi taşıtın kolay ve emniyetli direksiyon kontrolünü garanti etmelidir.

► Maksimum 6 saniye içinde ön tekerlekler, 12 metrelik yarıçapa denk gelen dönme açı pozisyonuna getirilebilmelidir.► Eğer direksiyondaki tahrik kuvveti 250 N’un üzerinde ise güç desteği gereklidir.► Eğer böyle bir güç desteği arızalanırsa tahrik kuvveti 600 N’nu aşmamalıdır.► Tahrik kuvveti merkezden (hidrolik direksiyon sistemi gibi) son duruş konumuna kadar uyumlu olmalı ve azalmamalıdır. (Notları, 2012)► Taşıtın doğru olarak sürüşü mümkün olmalı, olağandışı direksiyon düzeltmeleri olmamalıdır.► Mekanik parçalarda boşluk olması izin verilmeyen bir durumdur.► Mekanik iletim elemanlarının bütünü, kullanım sırasında oluşan tüm yükleri ve gerilimleri karşılayabilmelidir.► Tümseklerin, engellerin üzerinden geçmek gibi alışılmadık sürüş manevraları sırasında, kaza gibi olaylara sebep olabilecek herhangi bir kırılma ve çatlama sonuçlara yol açmamalıdır.  

Şekil 1: Trapez mekanizması

 

Günümüzde en çok kullanılan direksiyon sistemi, Ackerman geometrisi sistemidir. Bu sisteme göre yapılmış olan bir direksiyon sistemi üç kısımdan oluşur;

1) Direksiyon simidi ve mili,2) Direksiyon mekanizması,3) Tekerlekleri mekanizmaya bağlayan çubuk sistemi.

Direksiyon sistemleri, tasarım açısından farklılık gösterseler de işlevsel açıdan benzerlerdir. Örneğin orta rod kolunun tekerlek merkezinin ötesine yerleştirildiği sistemlere, önden dümenleme sistemi denir. Ackerman koşulunun en iyi uygulandığı sistem trapez mekanizmasıdır (Şekil 1). Bu sistem geometrisindeki asimetriklik sağa veya sola dönüşlerde dönüş yönüne göre viraj içindeki tekerleğin daha fazla sapmasını sağlar. Ayrıca Ackerman geometrisi de taşıtın aks aralığı ve ön aks genişliği fonksiyonunun birer parametresidir. 

Düzlemsel hareket yapan bir taşıtın dönüş hareketi esnasında her tekerleği bir yay üzerinde hareket etmektedir. Dönüş esnasında taşıt kararlılığını korumak ve minimum tekerlek aşınması sağlamak için tekerleklerin kaymadan yuvarlanmasını sağlamak gerekir. Bu da tekerleklerin taradıkları yayların merkezinin yani ani dönme merkezlerinin çakışık olması koşulundan geçer. Başka bir tarifle ani dönme merkezinden tekerleklerin izdüşümlerine uzatılan ışınlar, tekerlek izdüşümüne dik olmalıdır. Bu duruma ideal dönüş geometrisi veya Ackermann geometrisi adı verilir. Ackermann geometrisindeki tekerlek sapma açıları taşıt iz genişliği (w), aks aralığı (l) ve dönüş yarıçapına (R1) göre formüle edilebilir. 

Şekil 2: Ackerman geometrisi

Ackermann geometrisinden elde edilen formüllere bakıldığında taşıtın dönüş yarıçapını belirleyen değişkenler tekerleklerin dönüş açıları, aracın aks aralığı ve iz genişliğidir. Bu parametrelerden aks aralığı belirlenirken taşıtın ağırlığı, ağırlık merkezinin yeri ve aksların taşıma kapasitesi gibi parametreler birincil rol oynamaktadır. Dümenlemeye olan etkisi ikinci planda kalmaktadır ve dümenlemeyi iyileştirmek için değiştirilmesi uygun değildir. İz genişliği de yalnızca iç ve dış tekerin dönüş açıları arasındaki farkı belirleyen parametredir. Dönüş yarıçapının azaltılması için değişiklik yapılabilecek tek parametrenin tekerleklerin dönüş açıları olduğu görülür. 

Şekil 3: Teorik ve gerçek dönme açıları

Çok akslı taşıtlar için ackermann geometrisini yakalayabilmenin koşulu tüm akslardaki tekerlekleri uygun açılarda döndürmektir. Tüm aksların tekerleklerinin saptırılamaması durumunda ackermann geometrisini sağlayabilmek adına ancak bir tane aksın tekerlekleri sabit kullanılmalıdır. Tek aksının tekerleklerinin sabit tutulduğu üç akslı bir taşıt için ackermann geometrisi Şekil 4’de gösterilmiştir. Bu taşıt için tekerleklerin dönme açıları aşağıdaki formüllerle ifade edilebilir. 

Şekil 4: İki aksı dümenlenen bir taşıtın ackerman geometrisi

Sağlıklı bir dönüş için bu ideal açıların gerçekleşmesi, tam olarak olmasa da, araçtan beklenen manevra cevabına göre belirlenen bir yaklaşık değer, iki tekerlek arasına kurulan mekanizmalar yardımıyla sağlanır (direksiyon mekanizmaları). Direksiyon mekanizması daha önce de söylendiği gibi, Ackermann koşulundan fazla uzaklaşmayacak şekilde iç tekeri, dış tekerden daha fazla saptırmalıdır. Dolayısıyla mekanizmayı oluşturan rod kollarının boyları ve uzaysal konumları önemlidir. 

Dört tekerlekten yönlendirme virajlarda yol tutuşunu arttıran, yüksek hızlarda araçların emniyetli ve kolay sollanmasını sağlayan, şehir içindeki manevraları ve park etmeyi kolaylaştıran bir sistemdir. İlk 4ws sistemi 1905 yılında Lotil marka traktörde uygulanmıştır. Honda 1987 yılında mekanik kumandalısını, Mazda ise 1988 yılında elektronik kumandalısını piyasaya çıkarmıştır. Ön tekerlekleri sağa veya sola kırdığımızda arka tekerlekler de ön tekerleklerin 5'te 1'i kadar sağa veya sola dönerek arabanın arkasının viraj dışına doğru kaçmasını engeller. Yüksek hızda arka tekerlekler ön tekerleklerle aynı yönde düşük hızlarda ters yönde dönmektedirler. 

Şekil 5: Ön ve arka akstan dümenlenmiş araç

Bu uygulamada ön ve arka tekerleklerin merkezinden tekerleğe dik çıkan ışınlar, sabit olan orta aksın tekerleklerinin merkezinden uzanan ışını tek bir noktada kestiğinde Ackerman geometrisine uygun dönüş sağlanabilir (Şekil 5). Ön ve arka aksın iç ve dış tekerleklerin dönüş açıları kendi içlerinde orta aksa olan mesafeleriyle ters orantılıdır. 

Şekil 6: İlk ve son aksının tekerlekleri dümenlenmiş araç

Bu uygulamanın en belirgin avantajı dönüş yarıçapının çok büyük ölçüde düşürülmesidir. İz genişliği 2300 mm, birinci aks aralığı 1530 mm ve ikinci aks aralığı 1644 mm olan örnek üç akslı aracın, birinci ve üçüncü aksının dümenlendiği konfigürasyonla, ilk iki aksının dümenlendiği konfigürasyonun dönüş yarıçapları açısından kıyaslanması Çizelge 3.1 de verilmiştir. 

Bu önemli avantajına rağmen birinci ve sonuncu aks tekerleklerini ters yöne saptıran bu konfigürasyonun önemli bir dezavantajı vardır. Arka tekerlekleri saptırılan taşıt seyir dinamiği bakımından kararsızdır. Bu taşıtlarda dönme esnasında direksiyon bırakıldığında taşıtın saptırılmış arka tekerlekleri doğrulacağı ters yöne doğru git gide küçülen bir yörünge izler. Bu yüzden yüksek hızlarda arka direksiyon tertibatı kilitlenmelidir.

İkinci uygulama ise kamyonlardaki ikiz dümenlemeye benzer biçimde öndeki iki aksın tekerleklerinin saptırılmasıdır (Şekil 7). Kullanılan sistemin yapısı araçların bağımsız süspansiyon, katı aks oluşuna göre, gövdesinin şasili veya monokok oluşuna göre farklılık gösterir. 

Şekil 7: Ön iki akstan tahrikli sistem 

Altı tekerlekli taşıtlarda çift akstan dümenlemenin, tek akstan dümenlemeye göre avantajları şunlardır:

► Aks başına düşen statik yük azalacağından, aksta oluşan statik ve dinamik gerilmeler de önemli ölçüde azalır.► Özellikle engebeli yol koşullarında tek akstan dümenlemeye göre yol tutuşu üstündür.► Dikey momentin akslar arasında paylaşılmasından ötürü tekerleklere gelen ani şoklar ve devamındaki titreşimlerde azalma meydana gelir.► Dümenlenen akslardan sadece birinin hasar görmesi, dümenleme fonksiyonunun devam etmesini engellemez. Güvenilirliği tek akstan dümenlemeye göre yüksektir.► Ackermann prensibine uygun açılar yakalandığından aynı aks yükleri için tek asktan dümenlemeye göre sürtünmeler ve tekerlek aşınmaları azalır.

Kaynak:

►Burha, M. ( Haziran 2010). İki Akstan Dümenlenen Üç Akslı Özel Maksatlı Bir Taşıtın Direksiyon Mekanizmasının Kinematik Tasarımı. İstanbul: Yüksek Lisans Tezi.►Notları, D. (2012). Taşıt Dinamiği. Afyon: Afyon Kocatepe Üniversitesi. 

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Ackerman family | Attack on Titan Wiki

Ackerman family

Levi and Mikasa, the only known living members of the Ackerman family

Name

Ackerman familyアッカーマン家Akkāman-ke

Known members Living members Deceased members
7 2 5

Notable features

Bloodline of warriors, "awakened power"; Kenny was an infamous serial killer; Levi is regarded as Humanity's strongest soldier; Mikasa ranked top of her trainee group

The Ackerman family (アッカーマン家 Akkāman-ke?) is one of several families that live within the Walls. They were traditionally a bloodline of warriors close to the crown, but after refusing to follow the ideology of the First King, they suffered intense persecution from the monarchy that left them on the brink of extinction.[1] There are currently only two known living members left.

    History

    The Ackermans were one of the families that lived in the world prior to the raising of the Walls.[2] At some point in their history, they gained an awakened power as "byproducts of Titan science".[3] They were acknowledged as a bloodline of warriors close to the crown[4] and acted as the monarchy's right hand entrusted with humanity's survival;[2] probably thanks to the "awakened power" characteristic of their bloodline (see Awakened power). Some members of this family survived the Great Titan War that ended more than 100 years ago and moved within the Walls that King Fritz created for the Eldians.[5]

    After the King erased the memories of the people inside with the power of the Founding Titan, the Ackermans were one of the few bloodlines that were unrelated to the Subjects of Ymir and were therefore immune to this mental manipulation; others include the Asian clan[6] and those who would become the noble families.[7]

    Kenny meets Uri, the latter promising to stop the purges

    However, along with the Asian bloodline, they refused to follow the King's ideology of a world ruled by Titans as the true peace[8] and gave up their status in order to turn their backs on the monarchy.[9] Fearing his inability to control them,[10] the King plotted a persecution against them, bringing both races to the brink of extinction.

    At the end, the head of the Ackerman family offered his own life to ensure the survival of the bloodline and was executed. The rest of the generation avoided telling their children about humanity's lost memories in order to protect them from the monarchy's purge.[11] As a result, the following generations grew up without that knowledge.

    Nevertheless, not even this stopped the oppression on them, and several generations later the Ackermans were still pursued, with some of them seeking refuge in the Underground City[12] and others fleeing to the mountains at the edge of the Wall.[13]

    The human hunting only stopped after Kenny Ackerman met the then King Uri Reiss, with the latter apologizing for the actions of the prior monarchs, stopping the persecution, and accepting Kenny as his right-hand man.[14]

    Awakened power

    Levi strikes out at the Beast Titan

    Along with their immunity to mental manipulation, a special ability displayed by some members of the Ackerman family is a kind of "awakened power" not seen in any other bloodline so far. This ability is described by Levi Ackerman as "knowing exactly what needs to be done".[15] Users of this power exhibit physical abilities far above the average soldier and human, such as superhuman strength, speed, agility, accuracy, and coordination. The origins of these abilities are unknown except for the fact that they are a "byproduct of Titan science".[16]

    In consequence, these users are acknowledged as extremely powerful warriors, Levi being known as "Humanity's Strongest Soldier",[17]Mikasa Ackerman as the best soldier of her generation[18] and "as valuable as a hundred average soldiers",[19] and Kenny Ackerman being considered by Levi as even more dangerous than himself[20] and capable of killing more than 100 members of the Military Police without being caught.[21]

    Mikasa kills an Abnormal Titan

    This power does not seem to be present in all members (or at least not active) but arises when the person experiences certain moments in their life that awakens it and remains active for the rest of the user's life.

    The only Ackerman seen experiencing this moment so far is Mikasa, who was normal until the age of 9 when three human traffickers killed her parents and kidnapped her. After witnessing one of the kidnappers strangling Eren and being urged by him to fight, Mikasa awakened her dormant power and was able to kill the criminal with a single stab from the back that pierced his heart, displaying a level of speed, strength, and accuracy abnormal for a girl of her age; with the floorboards even snapping under her foot as proof of the immense strength she unleashed.[22]

    Levi stated that himself and Kenny also had similar moments that awakened their powers, though the exact circumstances are unknown.[23]

    Mikasa also experienced a drastic change in her personality after that event, going from being a somewhat cheerful girl to a much more serious and focused person very similar to Levi. However, it is unknown if this change in personality is related to the awakened power or to the trauma of losing her family.

    Members

    Alive

    Deceased

    Political members

    Deceased

    Trivia

    • The Ackermans are said to be traditionally a bloodline of warriors who acted as the right-hand men of the monarchs, and curiously enough, the three known "awakened" Ackermans have always ended up acting as the loyal right-hand men and bodyguards of someone: Mikasa follows Eren everywhere and is constantly trying to protect him, Levi follows Erwin and he is the only person Levi blindly trusts and obeys, and Kenny was for many years the bodyguard, right-hand man and close friend of Uri, whom he kept respecting even years after Uri's death.
    • "Ackerman" roughly translates to "Ploughman". As "Acker" is a germanic word for "ploughed field."

    References

    Navigation

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    Haider Ackermann - Luxury Fashion for Men

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    Ackerman Group

    The Ackerman Group provides a variety of services to safeguard our clients' employees and their families. By providing comprehensive protection against the full spectrum of threats, we provide an unparalled level of security.

    Our Risknet® service provides concise, up-to-the-minute analyses of risks in 100 countries. Risknet® is updated throughout the business day and can be accessed electronically worldwide around the clock. It consists of the following:

    Executive Digest

    Highly analytical reports give early warning of impending developments

    Country Summaries

    Summaries put risks into perspective

    Air Travel Guidance

    Analyzes information on latest terrorist risks concerning international travel

    City Guide

    Helps travelers navigate foreign cities

    Terrorist-group Glossary

    Provides information on major terrorist organizations

    Urgent Inquiries

    Clients with urgent inquiries are assured instant, 24-hour telephone access to our area specialists

    Customized Surveys

    Our analysts also are available for customized surveys and recommendations on countries or regions under consideration for new or expanded investment. Risknet® is included in Chubb Corporation's Kidnap/Ransom and Extortion insurance policy. You may also subscribe for a yearly fee

    Crisis Management Team Training:

    We offer a half-day training seminar designed specifically for members of a corporate Crisis Management Team (CMT). Guidance is provided as to the appropriate composition of the CMT and the management of key elements of a successful hostage recovery. Among the topics discussed are the handling of the notification of a kidnapping or extortion, management of relations with the victim’s family, liaison with law enforcements agencies, dealing with media, strategizing the negotiation, and organizing the ransom delivery and hostage recovery. The training also includes the presentation of a simulated kidnap case, which participants are tasked with resolving.

    Training Managers in High-Risk Areas:

    Individual or group training is given to executives, both expatriate and local, their families and staffs to improve their security practices, sensitize them to recognizing surveillances and prepare them to respond effectively to emergencies. Activity patterns of executives are analyzed in detail and recommendations are given for modifying them to mitigate risks.

    Protective Driving Training:

    Executives and/or their drivers are briefed on the conceptual basis for antiterrorist-driving methodology and instructed in techniques. We also conduct "hands-on" driving exercises both domestically and overseas.

    International Travel Security Awareness:

    It is neither possible nor necessary to provide protective details for the vast majority of executives who travel or reside overseas, so we place our major emphasis upon personal-security-awareness training. This half-day seminar surveys terrorist/criminal methodologies and explains "gray" - anonymous - travel, airline - selection strategies, airport safety guidelines, ground transportation alternatives, hotel security tips, tactics for avoiding street crime, means of protecting sensitive information and other countermeasures.

    Personal Security/Kidnap Prevention Training:

    This half-day classroom seminar is designed to train groups of expatriates and local nationals who live in high-risk environments. It focuses on personal responsibility for one’s own security, residential security guidelines, ground transportation security and route analysis for movements between residences and workplaces, and workplace security guidelines. It also describes basic hostile surveillance detection methodology that can be used in conjunction with behavior modification techniques.

    Hands-On Assault Survival Training:

    This half-day program is presented in conjunction with International Travel Security Awareness or Personal Security/Kidnap Prevention training. It adds an important element of live-action training in assault response. It features a combination of classroom instruction and “hands-on” training scenarios designed to introduce attendees to techniques for increasing their chances of surviving various assault scenarios, including express kidnappings, carjackings, ATM muggings, restaurant-invasion robberies and other criminal attacks. The training includes practical tips for employing appropriate verbal and body-language responses to mitigate the potential for violence.

    Workplace Violence/Active Shooter Training:

    This half-day seminar examines the phenomenon of violence in the workplace, stressing the importance of developing a comprehensive Workplace Violence Plan that focuses on both prevention and response tactics. The presenter describes a representative sample of case studies to examine typical perpetrator profiles and catalysts for violence. Also discussed are actions to be taken in response to an active shooter scenario, incorporating the tenets of “Run, Hide and Fight” set out by law enforcement. The final segment of the training focuses on appropriate after-action programs, such as psychological counseling for victims and other affected employees, potential litigation issues and tips for dealing with the media.

    Training Protective Personnel:

    We support our executive-protection strategizing with tailored, state-of-the-art training for protective personnel. The stress is on meticulous advance work, efficient personnel deployment and fluid crisis response.

    Physical Security Audits:

    Our consultants are prepared to conduct thorough physical security audits of corporate facilities, to include: office spaces, manufacturing facilities, warehouses, mining complexes, and executive residences. The audit assesses risks in and around the site and examines perimeter defenses, exterior lighting, parking facilities, building access controls and the competence of security guard services.

    We pride ourselves on our ability to arrange and oversee visits to high-risk areas throughout the world, and to protect personnel, meetings and special events.

    We are prepared to provide protective details, utilizing drivers and security escorts vetted and, in many cases, trained by our protection specialists. Transportation in soft (unarmored) or hard (armored) vehicles can be arranged as required.

    If the client so chooses, visits may be "advanced" and supervised by protection specialists on our staff. The credentials of our language- and area-qualified specialists are impeccable, and they stand ready to coordinate security, communications, logistics and protocol requirements.

    Our professionalism in responding to a wide range of corporate emergencies is broadly and enthusiastically acknowledged.

    Development of Contingency Plans:

    We are prepared to assist corporations in the formulation of crisis-management plans for kidnappings and other extortions, bomb-control guidelines and procedures for evacuating employees from unstable areas.

    Threat Evaluations:

    Our consultants travel at a moment's notice to evaluate threats levied by political or labor movements, or disgruntled or dismissed employees, calling upon psychiatric resources when necessary. They also arrange for the protection of the individual or asset at hazard.

    Hostage Recoveries:

    Our 24-hour availability assures immediate response to a kidnapping, and we are prepared to advise and assist the victim corporation through every aspect of the recovery process. Working under corporate decision-makers, we propose strategies, interface with law-enforcement authorities, handle negotiations, and protect and even deliver ransom funds - always with the objective of assuring the survival of the hostage.

    Extortion:

    We also are called upon to deal with monetary demands levied in connection with threats to harm an employee, damage a critical corporate resource, including a database or website, or contaminate a consumable product. Again, our reaction is immediate, our experience substantial and our paramount concern the protection of the client corporation's personnel and assets.

    Emergency Evacuations:

    We are ready to travel on short notice to assist in evacuating employees from areas that have turned hazardous. If necessary, we are prepared to employ unconventional extraction methodologies.

    Other Crises:

    Companies often find themselves unprepared to cope with those who would play hardball, especially in unfamiliar foreign climes. We help level the playing field.

    Our extensive network of investigative resources, developed and refined in the course of 35 years, covers not only the United States but extends to the farthest reaches of the globe. And our excellent relations with law-enforcement agencies, both domestic and foreign, facilitate investigative steps and, if required, criminal prosecutions.

    We approach all investigations in a prudent, deliberate manner. After analyzing clients' needs, we profer realistic strategies, ranging from the very basic to the exceptionally innovative. Often, a conservative approach is indicated, whereby we undertake an initial inquiry within a defined, reasonable budget. Its results and, when appropriate, suggested avenues of further exploration are presented to the client, who decides whether a fuller effort is warranted. Moreover, we add value to the information generated in the inquiry by collating it into a precise, perceptive, timely report.

    DUE DILIGENCE

    • Employment candidates, potential acquisitions and prospective joint-venture partners and franchisees
    • Review of criminal and civil history, credit history, financial data and history, education history, employment history, governmental and regulatory checks, social media, and reputation via interviews
    • Investigations conducted online and in-person; world-wide reach

    FRAUD

    • Direct financial losses, such as embezzlement or health insurance fraud
    • Indirect financial losses, such as kickback/bribery schemes, conflict-of-interest situations or bid-rigging/collusion
    • Product diversion investigations and surveillance operations

    CONVENTIONAL THEFT

    • Breaches of the production-distribution chain through inventory erosion, diversion, hijacking
    • Corporate penetration by criminal organizations

    UNDERCOVER

    • Placing experienced operatives inside client facilities to develop intelligence on thefts
    • Setting up reverse stings to expose criminally errant employees, vendors and distributors

    INTELLECTUAL PROPERTY

    • Market-watch programs
    • Controlled "buys" to identify retailers, wholesalers, importers and, ultimately, manufacturers of bogus goods

    COMPUTER FORENSICS AND CYBER INVESTIGATIONS

    • Data recovery from workstations, laptops and servers
    • Fraud and intellectual property theft; identity theft
    • Investigation and prevention of intrusions
    • Analyzing and documenting user access histories

    In a rapidly evolving cyber threat landscape, our comprehensive IT security audits have helped client corporations identify and remedy vulnerabilities in their computer networking systems and on their websites. Our experts have extensive experience in closing holes in computer networks, and limiting the opportunities for hackers to steal, corrupt or delete corporate information or hold it hostage in ransomware attacks.

    Our audits include assessments of and recommendations for your organization’s cybersecurity practices, including network infrastructure design, network perimeter protections, anti-malware and data leakage strategy, mobile device security, system security controls, backup and restoration processes, physical access controls, policies and procedures, and security management.

    Having audited a wide range of computer systems, we have a great breadth of experience from which to assess the degree to which a computer network conforms to industry best standards and practices. We also have on staff expert programmers, experienced in analyzing website vulnerabilities, and remedying them so that the websites are not hacked.

    When negative publicity is posted on the Internet about a person or corporation, we provide assistance in manipulating this information so that it is hidden or more difficult to locate. We also assist in tracing and identifying the individuals who have posted the information.

    www.ackermangroup.com

    The Ackermann Principle as Applied to Steering (Automobile)

    27.4.

    The Ackermann Principle as Applied to Steering

    27.4.1.

    The Ackermann Principle

    To achieve true rolling for a four wheeled vehicle moving on a curved track, the lines drawn through each of the four wheel axes must intersect at the instantaneous centre (Fig. 27.23). The actual position the instantaneous centre constantly changes due to the alternation of the front wheel angular positions to correct the steered vehicle’s path. Since both rear wheels are fixed on the same axis but the front wheel axles are independent of each other , the instantaneous centres lies somewhere along an imaginary extended line drawn through the axis of the rear axle.The Ackermann principle is based on the two front steered wheels being pivoted at the ends of an axle-beam. The original Ackermann linkage has parallel set track-rod-arms, so that both steered wheels swivel at equal angles. Consequently, the intersecting projection lines do not meet at one point (Fig. 27.24.). If both front wheels are free to follow their own natural paths, they would converge and eventually cross each other. Since the vehicle moves along a single mean path, both wheel tracks conflict continuously with each other causing tyre slip and tread scrub. Subsequent modified linkage uses inclined track-rod arms so that the inner wheel swivels about its king-pin slightly more than the outer wheel. Hence the lines drawn through the stub-axles converge at a single point somewhere along the rear-axle projection (Fig. 27.25).Fig. 27.24. Side-pivot steering with parallel-set track-rod arms. Fig. 27.25. Side-pivot steering with inclined track-rod arms. 27.4.2.

    Ackermann Linkage

    The self propelled motor vehicle almost from the beginning, used the double pivot wheel steering system. This was invented for horse drawn vehicles in 1817 by George Lankensperger, a Munich carriage builder. In England, Rudolph Ackermann acted as Lankensperger’s agent and a patent of the double-pivot steering arrangement was taken in his name.With this layout of the linkage the track rod arms are set parallel to each other and a track rod joins them together. In the straight ahead position of the steering, the linkage and axle beam forms a rectangle, but, as the stub-axles are rotated about their king pins, the steering arrangement forms a parallelogram. This linkage configuration turns both wheels the same amount. Figure 27.26A illustrates the parallel-set linkage positioned to provide both a 20 degrees and a 40 degrees turn for the inner and outer wheels.Charles Jeantand in 1878 introduced an improvement to the Ackermann linkage layout in which inclined track rod arms form trapezium (Fig. 27.25). This trapezium linkage configura­tion allows the inner wheel to rotate about its king-pin pivot by a greater amount than the outer wheel, which is necessary for providing semi-true-rolling (Fig. 27.26B and C). True rolling is obtained in the straight ahead position and on the left and right hand turns (locks). In between these three positions, only partial true rolling occurs. The degree of departure from true rolling and hence the amount of tyre scrub occurrence depends mainly on the ratio of track-rod to track-rod-arm lengths, and on the track-rod-arm angular inclination or set. In case the steering linkage dimensions and settings are carefully selected, a very little misalignment takes place for angle of turn up to about 15 degrees, beyond which the error increases rapidly. Also the deviation of the linkage from the theoretical true-rolling angles can readily be corrected by the tyre’s side-wall flexibility and tread distortion, provided the angular error between the steered wheels is small. Since the rear wheels turn on a smaller radius than the front wheels, it is easier to manoeuvre a vehicle in reverse than in the forward direction when parking.Fig. 27.26. Ackermann linkage geometry. A. Parallel set track-rod arms, outer wheel turned 20 and 40 degrees. B. 10 degrees set track-rod arms, outer wheel turned 20 degrees. C. 10 degrees set track-rod arms, outer wheel turned 40 degrees.27.4.3.

    Ackermann-linkage Geometry

    In parallel-set steering arms layout (Fig. 27.26A), the track-rod dimensions yi, xi andy0, x0, remain equal for all angles of turn. With the inclined arms (Fig. 27.26B and C), the inner-wheel track-rod end dimension yi, is always smaller than the outer wheel dimension y0, while negotiating a curve. On the other hand, there is very little variation between xi and x0 for small angular movements. For small steering angles about the king-pin up to say 10 degrees, there is very little difference between yi and y0 and between the inner and outer wheel turning angles.Figure 27.26B illustrates that for a 10 degrees set track rod arms if the outer wheel is turned at 20 degrees, then the corresponding inner wheel is shown to rotate 23 degrees. Similarly for the same set, for 40 degrees outer wheel turn, the inner wheel rotates 51 degrees (Fig. 27.26 C). Therefore, for a given angular movement of the stub axles, the inner-wheel track-rod arm and track-rod are more effective than the outer-wheel linkage in turning the steered wheel. For a given amount of transverse track-rod movement with inclined track-rod arms, the least effective angular displacement of stub-axle pivot occurs in the straight-ahead region, and the most effective angular displacement takes place as the stub-axles move away from the mid-position. Thus, the angular movement of the inner wheel relative to the outer wheel becomes much greater as both wheels approach movement of the inner wheel relative to the outer wheel becomes much greater as both wheels full lock (Fig. 27.27). With modern radial tyres, the difference between front and back-lock steering angles is sometimes reduced.Fig. 27.27. Front and back lock steering-angle curves. Fig. 27.28. Analytical solution diagram for Ackermann-linkage.

    Analytical Solution.

    If the slight inclination of the track rod (Fig. 27.28) is neglected, the movements of M and N in the direction parallel to the axle beam PQ can be considered as the same, say z. Let M’, N’ represent the correct steering position and, r, denote the cross-arm radius.

    Example 27.2. A track has pivot pins 1.37 m apart, the length of each track arm is 0.18 m and the track rod is behind front axle and 1.27 m long. Determine the wheel base which will give true rolling for all wheels when the car is turning so that the inner wheel stub axle is 60° to the centre line of the car. A geometrical construction may be used.Example 27.3. The distance between the king-pins of a car is 1.3 m. The track arms are 0.1525 m long and the length of the track rod is 1.2 m. For a track of 1.42 m and a wheel base of 2.85 m, find the radius of curvature of the path followed by the near-side front wheel at which correct steering is obtained when the car is turning to the right.Fig. 27.30. Graphical solution diagram for Ackermann-linkage. Fig. 27.31. Deflection of outer wheels for assumed deflection of inner wheel. Thus for the graphical representation of the steering mechanism on a paper of reasonable size with a sufficient degree of accuracy, it can be assumed that the steering arms are of definite length and make a certain angle with the longitudinal axis of the vehicle.Now determine graphically the deflection on the outer wheel, <|> for various assumed deflection of the inner wheels, say 0 = 10°, 15°, 20°, 25°, 30°, 35°, 40° and 45° for these steering arms as shown in Fig. 27.31.After knowing these values of 0, the correspond­ing angles 9 and $ are laid off on the opposite ends of the line C as shown in Fig. 27.32. A curve is then drawn through the intersection of lines describing the angle 9 and <j) correspondingly. The curve drawn is called steering error curve, because their devia­tion from true steering curve indicates the error in the steering angles. The angles 9 and § correspond­ing to the intersection of these two curves determine the correct steering angle for a particular a and c/b. If a is changed for the same c/b another steering error curve is obtained. Thus it can be concluded that theFig. 27.32. Steering error curve. most advantageous angle of the knuckle arms, i.e. a depends upon the turning range of the inner wheel.

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