Degrees of Freedom (Grübler)
Compute the degrees of freedom (mobility) of a planar mechanism by the Grübler-Kutzbach equation, DOF = 3·(n − 1) − 2·j1 − j2, where n is the number of links (including the fixed one), j1 the 1-DOF joints (pin, slider) and j2 the 2-DOF joints. A four-bar linkage (n=4, j1=4) has DOF=1: a single input motion controls the whole mechanism. The basis of mechanism and robot synthesis. Enter the number of links, 1-DOF joints and 2-DOF joints.
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Graus de liberdade (Grübler)
Quantos motores são necessários para controlar um mecanismo? A resposta é o número de graus de liberdade (mobilidade), dado pela equação de Grübler-Kutzbach para mecanismos planares: GL = 3·(n − 1) − 2·j1 − j2. Cada elo livre no plano tem 3 graus (x, y, rotação); o elo fixo tira a referência (n−1); cada junta de 1 grau (pino ou deslizante) remove 2 graus, e cada junta de 2 graus remove 1. O célebre mecanismo de 4 barras (n=4, j1=4) dá GL=1: um único motor de entrada comanda todo o movimento. GL=0 é uma estrutura rígida (treliça); GL negativo, uma estrutura hiperestática. É o primeiro cálculo na síntese de qualquer mecanismo ou robô. Informe o número de elos e de juntas.
Related Tools
Student's t Critical Value
Computes the critical value of Student's t distribution for the degrees of freedom and confidence level you choose, replacing the lookup in the t table at the back of statistics books. It returns both the two-sided value (for confidence intervals and two-tailed tests) and the one-sided value (for one-tailed tests). As the degrees of freedom grow, the value converges to that of the normal distribution. Enter the degrees of freedom and the confidence level.
Chi-Square Critical Value
Computes the critical value of the chi-square distribution for the degrees of freedom and confidence level you choose, dispensing with the printed table. It's the right-tail cutoff used in goodness-of-fit, independence and variance tests: if the computed statistic exceeds this value, the null hypothesis is rejected. Unlike the normal and the t, the chi-square is asymmetric and takes only positive values. Enter the degrees of freedom and the confidence level.
Jerk (Rate of Acceleration Change)
Compute the jerk, J = Δacceleration/Δtime, the rate of change of acceleration over time — the third derivative of position. High jerk causes jolts, vibration and wear; controlling it (jerk-limited or S-curve profiles) makes motion smooth, protecting mechanisms and improving the finish on CNC machines and elevators. Enter the acceleration change and the time interval.
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.