Position Complex Vector analytical method R2+R3-R4R1=0 l+lce:=le+lce Link lengths are known 4 is ground and is zero is input (independent variable)and is known Thus there are 2 unknowns,2 and 3 Position Complex Vector analytical method Solution Steps: 1.Substitute Euler identity into the equation 2.Separate resulting equation into real and imaginary parts.Set each to zero.Simplify by noting that 0=0 3.Isolate one of the two unknowns on the left side 4.Square both sides and add them-Simplify using the trigonometric identity:sin20+cos20 =1. This eliminates one of the variables 5.The remaining variable can be obtained by:Expanding and simplifying using the trigonometric identity: 1313 Position Complex Vector analytical method 1  2 0 3 i DC i AD i BC i AB l e  l e  l e  l e - - 0 R2  R3 R4 R1  • Link lengths are known • φ4 is ground and is zero • φ1 is input (independent variable) and is known • Thus there are 2 unknowns, φ2 and φ3 • Solution Steps: 1. Substitute Euler identity into the equation 2. Separate resulting equation into real and imaginary parts. Set each to zero. Simplify by noting that 4 = 0 3. Isolate one of the two unknowns on the left side 4. Square both sides and add them-Simplify using the trigonometric identity: sin2  + cos2  =1. This eliminates one of the variables 5. The remaining variable can be obtained by: Expanding and simplifying using the trigonometric identity: Position Complex Vector analytical method