5. Forward Analysis Problem Statement: given: constant mechanism parameters for example, for a 6R manipulator – link lengths a 12 through a 56 twist angles α 12 through α 56 joint offsets S 2 through S 5 the joint offset distance S 6 and the direction of the vector a 67 relative to S 6 in order to establish the 6 th coordinate system the location of the tool point measured in the 6 th coordinate system, 6 P tool the variable joint parameters for example, for a 6R manipulator – φ 1, θ 2, θ 3, θ 4, θ 5, θ 6

6. find: the location of the tool point measured in the fixed coordinate system, F P tool the orientation of the last coordinate system measured with respect to the fixed system,

7. Link Length, in. Twist Angle, deg. Joint Offset, in. Joint Angle, deg. a 12 =  12 =  1 = variable a 23 =  23 = S 2 =  2 = variable a 34 =  34 = S 3 =  3 = variable a 45 =  45 = S 4 =  4 = variable a 56 =  56 = S 5 =  5 = variable S 6 = free choice  6 = variable Mechanism Parameters for a 6R Robot

8. is defined by a 12, α 12, S 2, θ 2 … is defined by a 56, α 56, S 6, θ 6 is defined by φ 1