Calculus and Engineering Statistics

Is there anyone who could help me with this perfectly.

 

I want 100% on this one.

ENGR 210 Project

Due: Friday, August 2, 2013, 4:00 pm
Individual

A common analysis on the human body is to find the reaction forces and reaction moments at each joint.

To simplify the calculations, the joint/muscle system at each joint is treated as a fixed support during
a static analysis and each segment (body part from one joint to the next) is separated from the rest of
the body. The joints are considered fixed and not pins because the muscles work to counteract any
moments to keep the body part from rotating when holding in a static position (think carrying a box).

Keep in mind during this project:

*** All angles measured from the x-axis (θ1 is for upper arm, θ2 is for forearm and hand, θ3 is for the trunk)

*** The “forearm” is the lower arm (from the wrist to the elbow).

*** You will need to use your own height and weight and the tables on the last page to find the lengths,

weights, and center of mass (COM) for each segment (need to include the weight of the body
segment).

*** The object weight in the hand acts at the COM of the hand. Also, if you are just holding a weight in

your hand, is there ever an x-component? Think – which way are weights ALWAYS?

*** You can draw only one set of FBDs (draw general FBDs that will work for each situation), but be sure

to include variables for things such as the angles.

*** To simplify the lower back calculations, ignore shoulder-to-shoulder width. In other words, place both

shoulders in the same spot at the base of the neck (Like you are a stick figure where both arms
connect at the same spot at the top of your back!).

*** Remember you have two arms!!! 

What you should turn in:

1. Cover sheet with name, project title, class, date
2. Any FBDs used
3. Values used to calculate segment values (lengths, weights, COM)
4. Show your work for each method.

**You can use a computer program to help with the calculations. Be sure to include the
equations/code.

5. Values for each situation in a format that is easy to read/see all values at the same time so they
can be compared. Don’t just turn in the Excel file or the equations. You should have a table or
something else at the end that shows all the values for each situation (like a final answer). You do
not have to box this since there will be a lot – just an organized list.

6. Your comments on the values (what appears to be safer?, how should you carry a load?, etc.).
7. Make any additional comments on your “common sense” when carrying something. For example:

Which of the positions seems to be less tiring? Which position does not make sense if you were
carrying something with two hands? Etc.

Submit everything in Blackboard. If you use an Excel file, this DOES NOT have to be in the one pdf file with
everything else – it can be separate.

Required:

Find the reactions at the wrist, elbow, shoulder, and lower back while holding a 35 lb object with both

hands (each hand holds half) for the following situations and comment on the values you find. You
MUST separate each segment (e.g., must separate hand from forearm) and do not ever reattach the
segment (do not have the hand shown in the forearm FBD).

1. Start with upper arm straight down (θ1= -90
o
), forearm straight down (θ2 = -90

o
), and trunk (back

line) at an angle of θ3 = 75
o
. Find the reactions at the wrist, elbow, shoulder, and lower back.

Now, bend your arm only at the elbow (change the angle of the forearm and hand together) until
the lower arm is horizontal (as shown below in Figure 1). Change the angle in increments of 30

o
.

Find the reactions at the wrist, elbow, shoulder, and lower back for each angle change.

Figure 1. End position for #1 and #2

2. Repeat #1 with θ3 = 35
o
. Find the same values.

3. Start with upper arm at an angle of θ1= -60
o
, forearm at an angle of θ2 = -30

o
, and trunk (back line)

at an angle of θ3 = 75
o
(shown in Figure 2). Find the reactions at the wrist, elbow, shoulder, and

lower back.

Now, bend your arm only at the elbow (change the angle of the forearm and hand together) until
the forearm is horizontal. Change the angle in increments of 10

o
. Find the reactions at the wrist,

elbow, shoulder, and lower back for each angle change.

Figure 2. Beginning position for #3 and #4

4. Repeat #3 with θ3 = 35
o
. Find the same values.

*** There may be some calculations that are the same – make note of those and you do not have to
repeat them every time. Save yourself time – do not do more work than absolutely necessary, but do
show all work that is done.

Table 1. Body Segment Weights – multiply your total weight by the value to get the segment weight

Body Segment Female value Male value

Hand 0.0062 0.0067

Forearm 0.0152 0.0178

Upper arm 0.0281 0.0298

Trunk (including neck and head) 0.3780 0.3928

Table 2. Segement lengths – multiply your total height (in inches) by the value to get the segment length

Body Segment Female value Male value

Hand (wrist to finger tip) 0.098 0.108

Forearm (elbow to wrist) 0.1460 0.1510

Upper arm (shoulder to elbow) 0.1843 0.1877

Trunk (from lower back to shoulder)* 0.231 0.226

*Do not need length of neck and head

Table 3. Center-of-Mass (COM) locations (from given joint) – multiply the segment length by the value to

get the location of the COM (where the weight is located on the segment)

Body Segment Located from … joint Female value Male value

Hand Wrist 0.3427 0.3624

Forearm Elbow 0.4217 0.4172

Upper arm Shoulder 0.5322 0.5269

Trunk Lower back 0.89 0.89

Example of location of COM:

Forearm –

Wrist Elbow

Forearm length = height*0.1460 OR height*0.1510

Forearm weight = body weight*0.0152

OR body weight*0.0178

COM** = forearm length*0.4217 OR

forearm length*0.4172

** Notice: this is measured from the

joint listed in the table