A wrench is a system consisting of a single force and a single couple moment which is parallel with the force. Given a system consisting of N forces and M couple moments the goal is to reduce this to a wrench. To accomplish this requires four steps:

Find an equivalent force-couple system

Split the resultant moment into parallel and perpendicular components

move the wrench away from the axis to eliminate the perpendicular moment

1. Create a function named determineForceMoment which calculates the moment about a point caused by a force acting at another point. The function must:

input: F (force in Cartesian vector notation of size 1X3), mp ( coordinates of the point about which the force rotates of size 1X3), mp ( coordinates of the point at which the force acts of size 1X3)

output: Mf (the force moment in Cartesian vector notation of size 1X3)

use the points2vector function

2. Create a function named determineForceMoments which calculates the moments of an array of forces about some point

input: F - an array of cartesian forces (Nx3)

input: fp - an array of points at which each force acts (Nx3)

input: mp - the point about which the force rotates (1x3)

output: Mf - an array of force moments (Nx3)

must use the determineForceMoment function

3. Create a function named resultantForce which calculates the resultant Force of an array of forces. The function must:

input: an array of cartesian forces (Nx3)

output: a single resultant force (1x3)

4. Create a function named resultantMoment which calculates the resultant Moment given of an array of couple moments and force moments. The function must:

input: an array of couple moments (Nx3)

input: an array of force moments (Nx3)

output: a single resultant moment (1x3)

5. Create a function named equivalentForceCoupleSystem which calculates the resultant force and resultant Moment given an array forces and moments. The function must:

input: an array of forces (Nx3)

input: an array of couple moments (Nx3)

input: an array of force moments (Nx3) output: a single resultant moment (1x3)

output: a single resultant force (1x3)

must use the resultantForce and resultantMoment functions

6. Create a function named determineParallelPerpendicularComponents which calculates the parallel and perpendicular components of a given moment about the direction of a given force. The function must:

input: a single resultant moment (1x3)

input: a single resultant force (1x3) output: the parallel component of the moment (1x3)

output: the perpendicular component of the moment (1x3)

must use the vector2unit function

7. Create a function named determinePoint which calculates the point at which the wrench acts. The function must:

input: the resultant force (1x3)

input: the perpendicular moment (1x3)

input: the plane of interest: x=0 (1), y=0 (2), z=0 (3) output: the coordinate at which the wrench acts

8. Finally create a Program named wrench which calculates a wrench F~R and M~ and calculates the point at which it acts P(x, y,z). The program must use the determineForceMoments, equivalentForceCoupleSystem, determineParallelPerpendicularComponents,and determinePoint functions.

Fill in the following table using your program:

Case Couple Moments Forces Point fo r Force |Solve for point FRMi Oi - 50j + Ok 100i + 100j - 50k(0,0,1) (xy,0) o+07+25/ Oi + 0/+ 300k 450?+07+ok (3,4,0) (3,4,2) (0,4,3) 2 600i (xy,0) 50i + 30j +23k25i - 10j + 40k 121-15] + 23k 25+ 25% 20k 10'+10,-5k (5,3,4) (-2,-1,05) (x,0,z) -100+10% 30k Case Couple Moments Forces Point fo r Force |Solve for point FRMi Oi - 50j + Ok 100i + 100j - 50k(0,0,1) (xy,0) o+07+25/ Oi + 0/+ 300k 450?+07+ok (3,4,0) (3,4,2) (0,4,3) 2 600i (xy,0) 50i + 30j +23k25i - 10j + 40k 121-15] + 23k 25+ 25% 20k 10'+10,-5k (5,3,4) (-2,-1,05) (x,0,z) -100+10% 30k