Name: equivalent couples in mechanical systems
Uploaded: 2023-09-22T11:49:21.000Z
Duration: 1 min 28 s
Channel: JoVE

Considere uma válvula submetida a dois pares no mesmo plano tendo os mesmos momentos.
Se a magnitude, a direção e o sentido de rotação de seus momentos são os mesmos, os casais são equivalentes.
Primeiro, denote os pontos de interseção das linhas de ação dos dois casais.
Em seguida, mova as duas forças do primeiro casal para os pontos de interseção do segundo casal e resolva-as em componentes.
Um par de componentes tem a mesma magnitude, linha de ação e sentido oposto e pode ser cancelado.
Assim, o primeiro casal se reduz a um novo casal formado pelas forças S e -S.
Seu momento é igual ao momento da força S em torno de um ponto situado na linha de ação de -S.
Usando o teorema de Varignon, o momento do primeiro casal é igual à soma dos momentos de seus componentes, que por sua vez é igual ao momento do novo casal.
Assim, as novas forças são iguais às forças do segundo casal; implicando que os dois pares são equivalentes.
Da mesma forma, dois pares contidos em planos paralelos com os mesmos momentos também são equivalentes.

<ol>
	<li>Hibbeler, R.C. (2016). Engenharia Mecânica: Estática. Décima quarta edição, Nova Jersey: Pearson. Pág. 155.</li>
	<li>Meriam, J.L., Kraige, L.G. e Bolten, J.N.(2016). Engenharia Mecânica: Estática e Dinâmica. Oitava Edição, Cingapura: John Wiley & Sons. Pág. 50-51.</li>
	<li>Cerveja, F.P., Johnston, E.R., Mazurek, D.F., Cornwell, P.J. e Self, B.P. (2016). Mecânica vetorial para engenheiros. Décima primeira edição, Nova York: McGraw-Hill Education. Pág. 121-123.</li>
</ol>

acomplamentos equivalentes

Na engenharia mecânica, o conceito de acoplamentos equivalentes desempenha um papel crucial na compreensão e análise de vários sistemas mecânicos.

Dois acoplamentos são considerados equivalentes se produzem o mesmo efeito rotacional em um corpo rígido. Em outras palavras, os dois acoplamentos têm a mesma magnitude e atuam na mesma direção, causando o mesmo deslocamento angular ou aceleração no corpo.

Por exemplo, considere dois acoplamentos deitados no plano da página, sendo um deles composto por um par de forças iguais e opostas de magnitude de 30 N e uma distância perpendicular de 0,4 m entre elas. O outro acoplamento tem um par de forças iguais e opostas de magnitude de 40 N separadas por uma distância perpendicular de 0,3 m. Agora, o momento de cada par tem uma magnitude de 12 N·m, e ambos estão direcionados para fora do plano da página.

No segundo acoplamento, é necessário uma força maior para alcançar o mesmo efeito rotacional, uma vez que a distância entre as forças é menor.

Em muitos cenários da vida real, os sistemas mecânicos estão sujeitos a múltiplos acoplamentos simultaneamente. Ao identificar acoplamentos equivalentes, os engenheiros podem reduzir a complexidade do sistema e analisá-lo de maneira mais eficiente. Essa simplificação auxilia no projeto, solução de problemas e otimização de sistemas mecânicos.

Na engenharia automotiva, acoplamentos equivalentes são usados para analisar as forças atuantes em vários componentes do veículo, como sistemas de suspensão, eixos de transmissão e mecanismos de direção. Essas informações são vitais para o projeto e a otimização de veículos que oferecem desempenho e segurança ótimos.

Acomplamentos Equivalentes

Na engenharia mecânica, o conceito de pares equivalentes desempenha um papel crucial na compreensão e análise de vários sistemas mecânicos.
Dois casais ...

Education

JoVE Core

Mechanical Engineering

Engenharia Mecânica

Unit 1

Unidade 1

Force System Resultants

Resultantes de Sistemas de Forças

KEY TERMS AND CONCEPTS

TERMOS-CHAVE E CONCEITOS

Equivalent Couples

equivalent couples in mechanical systems

Equivalent couples in mechanical systems describe pairs of forces that create the same rotational effect on a rigid body. Two couples are equivalent when they have the same moment magnitude and act in the same direction. They then cause the same angular displacement or angular acceleration in the body.

A couple is made of equal and opposite forces separated by a perpendicular distance. The moment of the couple depends on both the force size and the spacing between the forces. For example, one couple can use 30 N forces spaced 0.4 m apart, while another can use 40 N forces spaced 0.3 m apart. Each pair produces a moment of 12 N·m, and both act out of the plane of the page.

The smaller spacing in the second couple means a larger force is needed to get the same turning effect. This idea helps engineers compare and simplify systems with more than one couple acting at the same time. By replacing multiple couples with an equivalent one, they can analyze the system more efficiently.

Equivalent couples are useful in design, troubleshooting, and optimization of mechanical systems. They also appear in automotive engineering when studying suspension systems, drive shafts, and steering mechanisms. This kind of analysis supports better vehicle performance and safety.

Equivalent Couples in Mechanical Systems

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principle of moments

Resolving Forces in Moment Calculations

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principle of moments: problem solving

Torque About an Axis in 3D Systems

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moment of a force about an axis: scalar

Bicycle Torque and Moment About an Axis

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moment of a force about an axis: vector

Torque on a Bicycle Wheel: Vector Method

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couple

Couple Moment in Force Systems

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equivalent couples

Equivalent couples in mechanical systems describe pairs of forces that create the same rotational effect on a rigid body. Two couples are equivalent when they have the same moment magnitude and act in the same direction. They then cause the same angular displacement or angular acceleration in the body. A couple is made of equal and opposite forces separated by a perpendicular distance. The moment of the couple depends on both the force size and the spacing between the forces. For example, one...

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simplification of a force and couple system i

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Resultant Forces in Force and Couple Systems

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simplification of a force and couple system: ii

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Resultant Force and Wrench Motion

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distributed loads

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Equivalent Resultant Loads on Beams

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key terms and concepts

Learn how equivalent couples create the same rotational effect in rigid bodies and how engineers use them to simplify mechanical and automotive systems.

Equivalent Couples in Mechanical Systems | JoVE K12

O JoVE Core Mechanical Engineering oferece vídeos animados concisos e de fácil compreensão que abrangem tópicos-chave como equilíbrio, forças, análise de treliças e mecânica estrutural. Explore suas aplicações no mundo real e observe esses conceitos em ação por meio de experimentos conduzidos por cientistas.

mechanical engineering

Equivalent Couples in Mechanical Systems

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