Max Acceleration (Cycloidal Cam)
Calculate the maximum acceleration of a cycloidal-motion cam follower, a_max = (2π·h·ω²) ÷ β², from the total lift h (mm), the cam angular velocity ω (rad/s) and the rise angle β (rad). Cycloidal motion is considered the BEST cam motion law for HIGH SPEEDS, and is standard in precision, high-rpm cams. Its decisive feature is that acceleration is a FULL SINE wave starting at zero, rising to a maximum, passing through zero, going to a minimum and returning to zero — i.e., acceleration is CONTINUOUS and starts and ends smoothly at ZERO at the ends, WITHOUT the discontinuities of SHM and parabolic. This means finite, continuous JERK, eliminating shocks and minimizing vibration excitation — the follower 'glides' smoothly without jolts. The price is a slightly HIGHER maximum acceleration than parabolic (2π ≈ 6.28 vs 4 in the factor) and SHM (π²/2 ≈ 4.93), but the dynamic SMOOTHNESS amply compensates at high speed. The name comes from the cycloid curve describing the displacement. Racing-engine valve cams, fast textile and packaging machines use cycloidal or derived (polynomial) profiles precisely to run at high rpm with low vibration. Enter the lift, the angular velocity and the rise angle.
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Aceleração máxima (came cicloidal)
A aceleração máxima do seguidor de um came com movimento cicloidal é a_max = (2π·h·ω²) ÷ β², a partir da elevação total h, da velocidade angular do came ω e do ângulo de subida β. O movimento cicloidal é considerado a melhor lei de movimento de came para altas velocidades, e é o padrão em cames de precisão e alta rotação. Sua característica decisiva é que a aceleração é uma senoide completa que começa em zero, sobe a um máximo, passa por zero, vai a um mínimo e volta a zero — ou seja, a aceleração é contínua e começa e termina suavemente em zero nas extremidades, sem as descontinuidades do MHS e do parabólico. Isso significa jerk finito e contínuo, eliminando os choques e minimizando a excitação de vibrações — o seguidor 'desliza' suavemente sem solavancos. O preço é uma aceleração máxima um pouco maior que a do parabólico (2π ≈ 6,28 vs 4 no fator) e que a do MHS (π²/2 ≈ 4,93), mas a suavidade dinâmica compensa amplamente em alta velocidade. O nome vem da curva cicloide que descreve o deslocamento. Cames de comando de válvulas de motores de competição, máquinas têxteis e de embalagem rápidas usam perfis cicloidais ou derivados (polinomiais) justamente para operar em alta rotação com baixa vibração. Informe a elevação, a velocidade angular e o ângulo de subida.
Related Tools
Max Acceleration (Parabolic Cam)
Calculate the (constant) maximum acceleration of a parabolic-motion (constant-acceleration) cam follower, a_max = (4·h·ω²) ÷ β², from the total lift h (mm), the cam angular velocity ω (rad/s) and the rise angle β (rad). Parabolic, or constant-acceleration, motion is the law producing the LOWEST possible maximum acceleration for a given lift and time — so it minimizes peak inertia forces. It consists of two halves: in the first, the follower accelerates with CONSTANT acceleration (rising parabolic displacement); in the second, it decelerates with the same constant (negative) acceleration, stopping at the top. The name 'parabolic' comes from the displacement diagram, formed by two parabolas. The great advantage is the low maximum acceleration; the drawback is that acceleration JUMPS abruptly — from +a_max to −a_max at the middle, and from zero to ±a_max at the ends — generating infinite JERK there, causing shocks, noise and vibration. So in practice pure parabolic is little used at high speed (despite low peak acceleration), and cycloidal or modified profiles that smooth these transitions are preferred. Parabolic is didactic and useful when peak acceleration is the limiting factor and speeds are moderate. Enter the lift, the angular velocity and the rise angle.
Max Velocity (Cycloidal Cam)
Calculate the maximum velocity of a cycloidal-motion cam follower, v_max = (2·h·ω) ÷ β, from the total lift h (mm), the cam angular velocity ω (rad/s) and the rise angle β (rad). In cycloidal motion, the follower velocity follows a smooth (1 − cosine) curve, starting from zero, reaching the MAXIMUM at mid-rise and returning to zero at the top — similar in shape to SHM, but with a slightly different profile ensuring acceleration continuity. The cycloidal maximum velocity (factor 2) is slightly HIGHER than SHM's (factor π/2 ≈ 1.57), reflecting that, to 'fit' the same lift in the same angle with smoother end accelerations, the mid velocity must be higher. Knowing the maximum velocity matters for the mechanism dynamics (the follower-mass kinetic energy, supplied then absorbed each cycle), for friction and wear at the cam-follower contact, and to check the system can follow the cam at high rpm. Comparing the maximum velocities and accelerations of the three classic laws (parabolic, SHM, cycloidal) is the basis of choosing the right cam profile per combination of load, speed and smoothness requirement. Enter the lift, the angular velocity and the rise angle.
Follower Max Acceleration (SHM)
Calculate the maximum acceleration of a simple-harmonic-motion cam follower, a_max = (π²·h·ω²) ÷ (2·β²), from the total lift h (mm), the cam angular velocity ω (rad/s) and the rise angle β (rad). Follower acceleration is perhaps the MOST important parameter in high-speed cam design, since it generates the INERTIA FORCES (F = m·a): the higher the acceleration, the greater the force the cam must apply to the follower (and the reaction back on the cam and bearings), the greater the tendency to vibration and follower 'jump', and the greater the contact stresses. In SHM, maximum acceleration occurs at the ENDS (start and finish of the rise), and — crucially — it has a DISCONTINUITY there (jumping from zero to maximum instantly), causing a shock and exciting vibrations. So for very high speeds, CYCLOIDAL motion is preferred (its acceleration is continuous, starting and ending at zero), despite cycloidal having a slightly higher peak acceleration. Acceleration grows with the SQUARE of the rotation ω — so doubling the rotation quadruples the inertia forces, and high-rpm engine cams are a design challenge. Enter the lift, the angular velocity and the rise angle.
The results provided by this tool are for general informational and educational purposes only and do not constitute professional, financial, medical, legal, tax or accounting advice. Always confirm important decisions with a qualified professional and official sources.