Analytical Algorithm of Designing Crank and Rocker Mechanism According to Travel Ratio Factor and Transmission Angle

There are many documents for designing the crank and rocker mechanism according to the given stroke speed ratio coefficient, but none of the problems of the transmission angle are considered. The size of the transmission angle has a great influence on the transmission performance of the mechanism. In many cases, the crankshaft mechanism has been proposed before its design. How can we meet the requirements? This solves the design problem of the crank-rocker mechanism that satisfies the stroke speed ratio coefficient and also satisfies the transmission angle. The expression of the analytical algorithm under four different conditions is introduced and can be used when designing.

1 basic equation based on transmission angle

Figure 1 Crank rocker mechanism minimum transmission angle position

Figure 1 shows a crank rocker mechanism. The lengths of crank AB, link BC, rocker CD, and stand AD are a, b, c, and d, respectively. The acute angle γ between the force F acting on the rocker CD by the crank and the force Fn in the rocker direction is the transmission angle. The smaller the γ, the worse the transmission performance of the mechanism, so there is a limit to the minimum γmin of the transmission angle. If the angle between the connecting rod and the pendulum is δ, when δ is an acute angle, γ=δ; when δ is an obtuse angle, γ=180°-δ. δ changes with the change of crank angle φ. From Figure 1 can be introduced:

(1)

According to formula (1), when δ=δmin or δ=δmax, the minimum transmission angle γmin occurs, and the transmission angles γ′ and γ′′ are set here.

(2)

γ′=δmin (when δmin<90°) or γ′=180°-δmin (when δmin>90°)

(3)

γ′′=δmax (when δmax<90°) or γ′′=180°-δmax (when δmax>90°)
The minimum value among γ′ and γ′′ is the minimum transmission angle γmin of the mechanism.
Formula (2), (3) can be introduced:
2ad-bc(cosδmin-cosδmax)=0 (4)

For the crank rocker mechanism shown in Fig. 2 (A and D are on the same side of C′C′′), the minimum transmission angle γmin is at φ=0, and δmin=γmin (see Reference 2).If γmin is known, Then δmin=γmin is known; if δmax is given again, equation (4) is the basic equation for a given transmission angle.

2 Basic equations given by the given ratio of travel ratios

Figure 2 Two-level position of crank rocker mechanism

Figure 2 shows the crank rocker mechanism in two extreme positions. The angle between C1D and C2D is the swing angle of the rocker; the AC1 and AC2 lines are the two collinear positions of the crank and the connecting rod; R is the radius of the circumscribed circle caused by the three points C1, C2, and P; h is D, O Distance between two points.
Let ∠C1C2A=α,α describe the position of point A in the center of crank rotation. In order to be able to satisfy the continuity condition of the mechanism movement, point A can only be Select on.
If the stroke speed coefficient is K and the angle between the poles is θ, then θ=180°(k-1)/(k+1).

(7)

Equations (5), (6), and (7) are basic equations obtained from the trip speed coefficient.

3 analytic algorithm expression

In Equations (4), (5), (6), and (7), if one of K, Ψ, δmax, δmin, and a, b, c, d is known, the other three can be found. Rod length. Here we introduce four different parsing algorithm expressions under known conditions. Due to space limitations, the derivation process is omitted and the results are only listed in the table below.

Analytic expression of table crank rocker

The analytical type can be directly used to design a crank lifter mechanism with a given speeding coefficient and transmission angle. It subtracts the cumbersome process of inspection and transmission, redesign and failure, and makes the design process simple, accurate, reliable, and can be operated on the machine with high efficiency.

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