CURRICULUM MECHANICS 1 CM / CALU Robotics Curriculum 1.0 © 2007

MECHANICS

Equation Sheet

Given ANY triangle

Law of Sines

or

Law of Cosines

or

Force

Torque

Center of Mass

a b csin sin sinα β γ

= = sinsin

βα=

ba

c a b ab2 2 2 2= + -( )cosγ a c b bc2 2 2 2= + -( )cosα

W mg= g = =32 2 9 81. . ft s m s2 2 f NsMax Static = µ f NkKinetic = µ F k L L kOSpring = - = δ

M dFAbout point =

1 1 2 2 3 3

1 2 3

+ += =

+ +

∑∑

i ii

ii

x Ax A x A x Ax

A A A A1 1 2 2 3 3

1 2 3

+ += =

+ +

∑∑

i ii

ii

y Ay A y A y Ay

A A A A

x b y h= =

3 3,

A bh=12

x b y h= =

2 2,

A bh=

x r y r= =,

A R=π 2

x r y r= =43π

,

A R=12

2π

Trigonometry

CURRICULUM MECHANICS 2 CM / CALU Robotics Curriculum 1.0 © 2007

MECHANICS

Equation Sheet

Statics

( )0 0 0a → → →

= = = ⇒ =F m m F

Inertia

I x axis( ) = 0 I I mly axis z axis( ) ( ) = =13

2 I I Ixy yz zx= = = 0

I x axis( ' ) = 0 I I mly axis z axis( ' ) ( ' ) = =1

122 I I Ix y y z z x' ' ' ' ' '= = = 0

I I mRx axis y axis( ' ) ( ' ) = =14

2 I mRz axis( ' ) =12

2

I I Ix y y z z x' ' ' ' ' '= = = 0

I mhx axis( ) =13

2 I mby axis( ) =13

2 I m b hz axis( ) = +( )13

2 2

I mbhxy =14

I Iyz zx= = 0

I mhx axis( ' ) =1

122 I mby axis( ' ) =

112

2 I m b hz axis( ' ) = +( )112

2 2

I I Ix y y z z x' ' ' ' ' '= = = 0

CURRICULUM MECHANICS 3 CM / CALU Robotics Curriculum 1.0 © 2007

MECHANICS

Equation Sheet

Constant Acceleration

v v a t t= + -( )0 0 0 s s v t t a t t= + -( )+ -( )0 0 0 0 021

2v v a s s2

02

0 02= + -( )

Conservation of Energy

KE PE W KE PE1 1 12 2 2+ + = +Non Conservative

KE m I= +12

12

2 2v ω PE kTorsion Spring =12

2θPE mgyWeight = PE kSpring =12

2δ