Explanation Given information: The machine consists of two toggles ABC and DEF which are operated by the hydraulic cylinder H . The toggles push the movable bar G forward, pressing the plate p into the cavity. The force which the plate exerts on the head is P = 12 kN . The angle θ = 30 ° . Assumption: Consider the state of member as the tension where the force is pulling the member and as the compression where the force is pushing the member. Consider the force indicating right side as positive and left side as negative in the horizontal components of forces. Consider the force indicating upside is taken as positive and downside as negative in the vertical components of forces. Consider the clockwise moment as negative and the anticlockwise moment as positive wherever applicable. Apply the equation of equilibrium wherever applicable. The segment FGC : Show the free body diagram of the segment FGC as in the Figure (1). Using Figure (1), Due to symmetry, the force which exerts on the head P is distributed to half on each joints F and C . F x = C x = P 2 (I) Substitute 12 kN for P in Equation (I). F x = C x = 12 2 F x = C x = 6 kN The member EF : Show the free body diagram of the member EF as in Figure (2). Using Figure (2), The movement at the point E : Determine the vertical reaction at joint F by taking the moment at the point E . ∑ M E = 0 F x sin 30 ° ( 200 ) − F y cos 30 ° ( 200 ) = 0 (II) Along the vertical direction: Determine the vertical reaction at the joint E by resolving the vertical component of forces. ∑ F y = 0 E y − F y = 0 (III) Along the horizontal direction: Determine the horizontal reaction at the joint E by resolving the horizontal component of forces. ∑ F x = 0 E x − F x = 0 (IV) Conclusion: Substitute 6 kN for F x in Equation (II). 6 sin 30 ° ( 200 ) − F y cos 30 ° ( 200 ) = 0 600 − 173

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Chapter 6, Problem 88P

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The force F in the hydraulic cylinder.

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Chapter 6, Problem 87P

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The force F in the hydraulic cylinder.

Solution Summary: The author explains the force F in the hydraulic cylinder. The machine consists of two toggles ABC and DEF which push the movable bar G forward, pressing the plate p into the cavity.

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The force F in the hydraulic cylinder.

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