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Determine system (machinery/ application).

  • Determine size, material and mass.
  • Determine coefficient of friction.
  • Calculate forces.
  • Calculate torque.
  • Calculate inertia.


Force

Normal Force $$F_N=m \cdot g$$
Acceleration Force $$F_a=m \cdot a$$
Gravitational Force $$F_G=m \cdot g$$
Frictional Force $$F_f=μ \cdot m \cdot g$$ $$=μ \cdot F_N$$
Compression Force $$F_p=p \cdot A$$
Spring Force $$F_s=k \cdot l$$



Torque

Torque = force ∙ arm $$M=F \cdot r \cdot sin⁡θ$$
Torque = moment of inertia ∙ angular acceleration $$M=J \cdot α$$



Inertia

Point $$J=m \cdot R^2$$
Solid Sphere $$J=\frac{2}{5} \cdot m \cdot R^2$$
Hollow Sphere $$J=\frac{2}{5} \cdot m \cdot \left(\frac{{R_1}^5-{R_2}^5}{{R_1}^3-{R_2}^3}\right)$$ Hollow thin-walled sphere: $$J=\frac{2}{3} \cdot m \cdot {R_1}^2$$
Solid Cylinder (1)$$J=m \cdot R^2$$ (2)$$J=\frac{1}{4} \cdot m \cdot R^2+\frac{1}{12} \cdot m \cdot L^2$$
Eccentric Solid Cylinder $$J=J_c+m \cdot {R_e}^2$$
Hollow Cylinder (1)$$J=\frac{1}{2} \cdot m \cdot ({R_1}^2+{R_2}^2)$$ Hollow thin-walled cylinder: $$J=m \cdot {R_1}^2$$ (2)$$J=\frac{1}{4} \cdot m \cdot ({R_1}^2+{R_2}^2+\frac{L^2}{3})$$ Hollow thin-walled cylinder: $$J=\frac{1}{2} \cdot m \cdot {R_1}^2+\frac{1}{12} \cdot m \cdot L^2$$
Circular Cone (1)$$J=\frac{3}{10} \cdot m \cdot R^2$$ Hollow thin-walled cone: $$J=\frac{1}{2} \cdot m \cdot R^2$$ (2)$$J=\frac{3}{20} \cdot m \cdot (R^2+4L^2)$$ Hollow thin-walled cone: $$J=\frac{1}{4} \cdot m \cdot (R^2+2L^2 )$$
Cuboid (1)$$J=\frac{1}{12} \cdot m \cdot (a^2+b^2 )$$ (2)$$J=\frac{1}{12} \cdot m \cdot (a^2+c^2 )$$ (2)$$J=\frac{1}{12} \cdot m \cdot (a^2+4c^2 )$$
Rod (1)$$J=\frac{1}{3} \cdot m \cdot L^2$$ (2)$$J=\frac{1}{12} \cdot m \cdot L^2$$