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A mechanism to convert uniform rotation to linear sinusoidal motion
3". Meehan/smsVol. 1, p. 83 Pergamon Press 1966. Printed in Great Britain
A MECHANISM TO CONVERT UNIFORM ROTATION TO LINEAR SINUSOIDAL MOTION Asst. Prof. JERALD M. H E N D E R S O N Department of Mechanical Engineering, University of California, David, California (Rece/ved30 August 1965) Abmtmet--The mechanism to be discussed here does the same thins as a Scotch yoke, but in a diffenmt manner. The only slider of this mechanism moves in the line of the linear sintmoidalmotion. Consequm2tly, when the mechanism transmits forces of appreciable magnitudes, it is not affected as much by wear and the resulting slap as is the transverse slider of a Scotch yoke. THE mechanism shown in Fig. 1 consists of two equal length cranks, AB and G F ; three finks, BC, CE, and EF; and a slider, D. The two cranks rotate in opposite directions with equal angular speed; 01 always has the same magnitude as 02, measured from an axis [3
! y x
E
Fu3. 1. parallel to the direction of the slider guides. Two of the links, BC and EF, are o f equal length; D is the midpoint of llnk CE; and the three together, that is ( B C + C E + E F ) , must have an extended length which exceeds the greatest distance between the crankpins B and F. This occurs when 01 and 02 are at the 90 ° position. Point D is constrained to move along the x-axis. Points A and G may be offset at equal distances from the x-axis. The uniform rotation o f the cranks causes D to have linear sinusoidal motion with a magnitude equal to the length o f crank AB. To show that the resulting motion of D is sinusoidal, first note that the magnitudes o f the y-coordinates of B and F are always equal. It follows then that triangles BCD and D E F are equal and that D always lies midway between B and F. Thus, since the x-coordinates o f B and F vary with the same sinusoidal motion, then D has sinusoidal motion. 83
A MECHANISM TO CONVERT UNIFORM ROTATION TO LINEAR SINUSOIDAL MOTION Asst. Prof. JERALD M. H E N D E R S O N Department of Mechanical Engineering, University of California, David, California (Rece/ved30 August 1965) Abmtmet--The mechanism to be discussed here does the same thins as a Scotch yoke, but in a diffenmt manner. The only slider of this mechanism moves in the line of the linear sintmoidalmotion. Consequm2tly, when the mechanism transmits forces of appreciable magnitudes, it is not affected as much by wear and the resulting slap as is the transverse slider of a Scotch yoke. THE mechanism shown in Fig. 1 consists of two equal length cranks, AB and G F ; three finks, BC, CE, and EF; and a slider, D. The two cranks rotate in opposite directions with equal angular speed; 01 always has the same magnitude as 02, measured from an axis [3
! y x
E
Fu3. 1. parallel to the direction of the slider guides. Two of the links, BC and EF, are o f equal length; D is the midpoint of llnk CE; and the three together, that is ( B C + C E + E F ) , must have an extended length which exceeds the greatest distance between the crankpins B and F. This occurs when 01 and 02 are at the 90 ° position. Point D is constrained to move along the x-axis. Points A and G may be offset at equal distances from the x-axis. The uniform rotation o f the cranks causes D to have linear sinusoidal motion with a magnitude equal to the length o f crank AB. To show that the resulting motion of D is sinusoidal, first note that the magnitudes o f the y-coordinates of B and F are always equal. It follows then that triangles BCD and D E F are equal and that D always lies midway between B and F. Thus, since the x-coordinates o f B and F vary with the same sinusoidal motion, then D has sinusoidal motion. 83