Analysis and Selection of Final Design

Kinematic Analysis

Kinematic and force analysis was performed in order to determine the forces needed in the system, specifically the forces necessary to maintain a grip on the object and to actuate the device. The elastic band that provides the closed state of the device will provide the gripping force. The device should securely close around an object and the grip must be maintained so that the object does not fall. The gripping force will vary based on the weight of the object to be picked. Since the design is voluntary open the user should not be required to provide any force to maintain this grip. The force provided by the user will open the prehensors when the user is prepared to pick or place the object. The force required by the user will vary based on the force of the elastic band as well as the location of the link. If the link is attached above the elastic band, the force required by the user will be greater than if the link is attached below the band.

Gripping Force:

Sum of Forces = 0 for the grip to be maintained on the object. The grip force includes a tangent and normal force on both sides of the object (two prehensors); these forces must balance the weight (m*g) of the object.

Therefore:

N + T = F

∑F = 2N + 2T – m*g

28 Where:

F_grip is the gripping force

∑F is the sum of all forces N is the normal gripping force T is the tangential gripping force m is the mass of the object

and g is the acceleration due to gravity

From this equation the sum of the forces in the x and y directions can be calculated.

∑F

= 0 = 2N

– 2T

∑F

= 0 = 2N

+ 2T

– (m*g) = 2*N*sin(θ) + 2*T*sin(90-θ) = m*g

Where:

θ = the angle between the normal and x axis, this is dependent on the size of the object to be gripped

The force of the elastic band must therefore be equal to or greater than the force of the grip to ensure the grip is maintained on the object.

Therefore:

F

= F

Dynamic Analysis:

A kinematic drawing of design II is shown in Figure 18 below. This drawing is of the linkage system that actuates the device when a force is applied by the user.

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Figure 18 - Kinematic outline of Design II

The “ground” link (link 1) is the distance between the two fixed pivoting points of the system. One is where the wrist attachment is secured to the aluminum bar and the other is where the pivoting prehensor is attached to the fixed prehensor. Link 2 in the figure is the wrist

attachment or actuator of the device. This is the link that wraps around the users wrist where the user can apply the actuating force to open the prehensors. Link 3 is the link that connects the wrist attachment and the pivoting prehensor. Finally link 4 is the pivoting prehensor. The subscripts in the image refer to the four links. There are two external forces applied to the

system: the force of the user and the force of the elastic band. Each link in turn applies a force on a connecting link based on these external forces. For example link 2 applies a force on link 3, this is equal in magnitude to the force that link 3 applies to link 2. In order to better understand all the forces kinematic drawings of each link were created.

30 Link 2 (wrist attachment / actuator)

Figure 19 shows the kinematic drawing of link 2. The forces include: F_user, the force required by the user to actuate the device, as well as F21 and F23, the forces that link 2 apply on links one and three respectively. The figure also includes the position vectors (R) of each force.

The position vectors begin at the center of gravity of the link shown in the image as CG2 and extend to where each force is applied on the link. The center of gravity is also the point where the weight (m*g) of the link is applied.

Figure 19 - Link 2 with applied and joint forces

We know from Newton’s second law that the sum of all forces (F) equals to the product of mass (m) and its acceleration (a) for mechanical translation and the sum of all torques (T) equals to the product of the moment of inertia (I) and the angular acceleration (α) of the link in rotation.

∑F = m*a (where a in this case is g)

∑T = I*α

31 From the drawing of link 2 in Figure 19 the following equations were derived:

∑ F = F

+ F

+ F

= m

g

∑ Τ = Τ

+ (R

x F

) + (R

x F

) + (R

x F

) = I

α

From these equations we get 3 equations:

F

= F

- F

- F

= m

g

32 Therefore:

F

= (-)F

- F

= 0 F

= F

+ F

= 0.006 lb Τ = Τ

+ (0.5in * F

) + (0.5in * F

)

A similar analysis was performed on links 3 and 4.

Link 3 (Link)

From the drawing of link 3 in Figure 20 the following equations were derived:

∑ F = -F

+ F

= m

g

∑ Τ = (R

x F

) + (R

x F

) = I

α

33 From these equations we get the following 3 equations:

F

= - F

+ F

= m

g

F

= - F

+ F

= m

g

Τ = (R

F

– R

F

) + (R

F

- R

F

) = I

α

Knowns:

m3 = 0.006lb / g = 0.006 lb / 384 in/s² gx = 0

g_y = 32 ft/s² = 384 in/s² R3 = 3.29 in

R₃₂ = 1.645 in R34 = 1.645 in Therefore:

F

= - F

+ F

= 0 F

= - F

+ F

= 0.006 lb

Τ = (1.645in * F

) + (1.645in * F

) = 0

34 Link 4 (Pivoting Prehensor)

From the drawing of link 4 in Figure 21 the following equations were derived:

∑ F = F43 + F₄₁ + F_elastic = m₄ g₄

∑ Τ = Τ41 + (R43 x F43) + (R 41 x F41) + (R elastic x Felastic) = IGα4

From these equations we get the following 3 equations:

F

= F

+ F

+ F

= m

g

F

= F

+ F

+ F

= m

g

Τ = Τ

+ (R

F

– R

F

) + (R

F

– R

F

) + (R

F

– R

y

F

) = I

α

Knowns:

m₄ = 0.006lb / g = 0.006 lb / 384 in/s² gx = 0

gy = 32 ft/s² = 384 in/s²

Figure 21 - Link 4 with applied and joint forces

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This list of nine equations relates the force required by the user to the force of the elastic band.

36

Weighted Decision Matrix

The two preliminary designs were compared using a weighted decision matrix. From the design specifications, five major requirements were chosen as the most prevalent for this design.

These five requirements were given definitions as they pertain to the project as well as relative weights based on which requirements were considered the most important. The five requirements and their definitions and weights are shown in Table 1 below.

Table 1 – Requirement definitions and their relative weights Requirement Weighting

Factor

Relative Weight

Definition

Portability 20% 0.20 How easily the product can be carried around, how well the client can move around with the product

Ease of Use 25% 0.25 How easy the product is to operate, how easily the device can be set up

Lightweight 10% 0.10 Product weighs less than 5 lbs.

Safety 25% 0.25 How secure the product is attached

Repeatability 20% 0.20 Product is able to withstand many cycles and able to grip different shaped and sized objects

Values were assigned to each preliminary design for each requirement on a scale of one through five where one signifies a design that is considered insufficient, and five, a design that is excellent. The values were determined by comparing the products to each other. As depicted in Table 2 preliminary design II was chosen and a prototype was constructed.

37 Table 2 - Decision Matrix

Selection of Materials

The gripping component of the device was 3D printed and ABS plastic was chosen as the material. ABS plastic is an industrial thermoplastic that is commonly used in industry. The tensile strength of this material is 37 MPa. This material can be printed in low or high density.

High density was chosen to ensure the parts could withstand the forces necessary to actuate and maintain the grip of an object.

Aluminum was selected because it is a metal commonly used to create other adaptive devices based on its lightweight and consistent reliable strength [17]. It also was beneficial for this project because it was inexpensive and simple to machine into the necessary parts.

The Velcro straps were selected because they can easily be secured and detached with very minimal force, to ensure the client could attach and use the device on his own.

Analysis was performed in this chapter and the preliminary designs were compared using a weighted decision matrix. Design II was chosen as the final design and materials were selected.

The following chapter discussed the manufacture and testing of the prototype of this design.

Requirement Weight Prelim Design I Prelim Design II

Portability 0.20 3 4

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