Mechanisms Final

• a pure fourbar linkage (oscillation)
• a fourbar slider-crank (translation)

• requires an external force to keep the cam in contact with the follower
• a spring usually supplies this force

• closed by joint geometry
• slot milled out of cam
• no external force required

produces infinite acceleration and infinite jerk

produces infinite jerk

produces infinite jerk

• Cycloidal Displacement
• Sinusoidal Acceleration
• Modified Trapezoidal Acceleration
• Modified Sine Acceleration

B.C.: v=0 at theta=beta (to match zero velocity of the dwell)

• lower peak acceleration better
• lower peak velocity better
• smoother jerk means lower vibrations
• acceleration and velocity are higher than other functions

• finite jerk
• higher accceperation

Advantage: lowest magnitude of peak acceleration of standard cam functions (lowest forces)

• lowest peak velocity (lowest kinetic energy)
• smoother jerk

• General form: s = C₀ +C₁x +C₂x² +...+C_nxⁿ
• where x = theta/beta or t
• the value of the rise and fall functions at their boundaries with the dwells must match with no discontinuities

• similar in shape to cycloidal
• discontinuous jerk because jerk unconstrained

• similar in shape to cycloidal disp
• set jerk to zero at 0 and beta
• Continuous and smooth jerk but everything else is larger

• Cycloidal
• 4-5-6-7 Poly
• 3-4-5 Poly
• Low jerk implies lower vibrations

• Modified Trapezoid
• Modified Sine
• 3-4-5 Poly
• Low accelerations imply low forces

• Modified Sine
• 3-4-5 Poly
• Low velocity means low kinetic energy

use Modified Trap!

Smallest circle that can be drawn tangent to the physical cam surface.

smallest circle that can be drawn tangent to the locus of the centerline of the follower

locus of the centerline of the follower

• phi < 30 for translating follower to avoid excessive side load on the sliding follower
• phi < 35 for oscillating followers (on a pivot arm) to avoid undesirable levels of pivot friction
• Increasing the prime circle radius (R_p) will reduce phi

• perpendicular dist. btw follower's axis of motion and center of cam
• can be used to correct asymmetry in max and min phi

• Start with R_p = 3*h , h= max lift
• compute phi for all theta
• iterate to acceptable condition
• for translating roller follower maximum pressure angle should be < = 30 deg
• eccentricity can be introduced to correct asymmetry in max and min phi

• minimum radius of curvature occurs near the point of minimum acceleration (maximum negative acceleration)
• rho can only be controlled with R_p once s, v, a are defined

• If | rho | < R_f : Undercut due to small negative rho => BAD!
• Undercut due to small positive radius of curvature creates a cusp => ALSO BAD!
• If |rho| = R_f : Undercutting => BAD!

Can't have a negative radius of curvature

• The involute is a curve that can be generated by unwrapping a taut string from a cylinder (called the evolute).
• The string is always tangent to the cylinder
• The center of curvature of he involute is always at the point of tangency of the string with the cylinder
• A tangent to the involute is always normal to the string, the length of which is the instantaneous radius of curvature of the involute curve.

size of teeth must be the same for both gears

• center distance errors do not affect the velocity ratio
• as the center distance increases so will the pressure angle and vice versa
• in involute gears the pressure angle remains constant between the point of tooth engagement.