The eye prototype used to test the connection between two servos and Autodesk Maya is a simple design in which the eye can only rotate left and right. This means that the eye has 1 degree of freedom (DOF), able to move along 1 axis.
For the eyepot animatronic, I would like to have it look up and down (Pitch) and left and right (Yaw). The eye would need 2 DOF. Adding a third DOF would give the eye the ability to roll, this also means that we need another joint. But what does this all mean?
Figure 1. Different degrees of freedom (DOF) (Own work)
Degrees of freedom
Degree of freedom, or in short DOF is a term often used in mechanical engineering and robotics describing the number of directions something can move.
"DOF is defined as the minimum number of independent variables required to define the position of a rigid body in space. In other words, DOF defines the number of directions a body can move."
(What Is Degree of Freedom (DOF) in Mechanics, 2020)
A plane has 6 DOF. The first 3 DOF are translating forward and backward, up and down, left and right. The other 3 DOF are Rolling, Yawing, and Pitching.
Figure 2. Airplane movement Roll, Yaw, and Pitch.
Not everything can move in 6 DOF. The knee, for example, has only 1 DOF. A part of the human body with 2 DOF is the ankle, and an example of 3 DOF in the human body would be the neck; You can roll, yaw, and pitch it. Try it!
Mechanisms often have more than 6 DOF; this is the total amount of DOF the machine has, not just one joint.
Figure 3. Example of 3 degrees of freedom in the human body.
In the human body, the DOF is determined by the type of joint. Different types of joints allow motion in some directions and constrain it in others.
Figure 4. Joints in the human body.
Knowing the DOF helps to pick out an appropriate type of joint.
Joints
Joints can be divided into three different categories.
Lower pair joints
Higher pair joints
Compound joints
The third category is a combination of two or more lower and or higher pair joints. The difference between lower and higher pair joints has to do with contact stress. As this subject is out of my graduation scope, I suggest reading this if you would like to know more.
The following list provided by (Types of Kinematic Joints in the Design of Machines, 2008) are examples of joints per category.
1. Lower pair joints
- Revolute/Hinge Joint, 1 DoF
- Prismatic/Slider Joint, 1 DoF
- Srew/Helical Joint, 1 DoF
- Cylindrical Joint, 2 DoF
- Spherical/Ball Joint, 3 DoF
- Planar Joint, 3 DoF
2. Higher pair joints
- Cylindrical roller, 1 DoF
- Cam pair, 2 DoF
3. Compound joints
- Ball or Roller Bearings, 1 DoF
- Universal joint, 2 DoF
Choosing a joint for the eye
To make the eye rotate along 2 different axis, we need a mechanism with 2 rotational DOF. Since current circumstances make it difficult to get mechanical parts, I decided to use a ball joint for the first test since it is possible to 3D print it.
Ball joint
A ball joint, or ball-and-socket like the one in the shoulder, has 3 DOF. Roll, Yaw, and Pitch. The third DOF, rolling, can be omitted since we won't be using it. In the human body, the ball and socket are kept in place by ligaments. The 3D print will have to stay in place by the plastic around it. I have 2 problems using the ball joint.
Figure 5. 3D printed ball joint.
The first problem is that I couldn't push the ball in the socket without damaging the socket. The socket's corners break while pushing the ball in. The PLA I'm using doesn't allow for much bending before snapping. The problem could be fixed using a different material or printing the ball and socket inside each other.
After I glued the corners back onto the socket, I encountered a second problem. Although the joint has 3 DOF, it didn't rotate far enough as the corners were in the way. The corners are the ones that keep the ball in place. Making the walls of the socket less high will allow for the ball to pop out easily. As I don't have a solution to this problem, I decided to go with a different joint.
Universal joint
The universal joint is a combination of two revolute or hinge joints, making it a compound joint. The U-joint in short has 2 rotational DOF; looking up and down (pitch) and looking left and right (yaw). Before buying an actual U-joint I 3D printed a U-joint from the website Thingiverse to see if it moved as I needed it to. Once the U-joint arrived I measured its dimensions and printed an eye and a base.
The U-joint prototype consists out of 3 parts. The eye, the base, and the U-joint itself. The eye is a simple sphere with four tiny holes on the edge for linkages to connect to. In the center of the eye, a pin is extruded that fits inside the U-joint. The U-joint connects to the pin of the base, which holds the eye up in the air while allowing it to rotate freely. The two pins are measured so that they don't collide with the U-joint when it rotates while making sure the pivot point of the joint and eye align.
Figure 6. U-joint prototype (Own work)
Since the U-joint gives me the motion without any problems, the rest of the design will be built around the use of a U-joint.
List of figures
Van den Brand, J. (2021, March 2). Different degrees of freedom (DOF) [Image].
airplane controll roll, pitch, yaw. (2016). [Animation]. Makeagif. https://makeagif.com/i/MybXwU
[3DoF]. (n.d.). adrienjoly. https://adrienjoly.com/vr/
Biodigital. (n.d.). joints in the human body [Illustration]. Thinglink. https://www.thinglink.com/card/974750001055924225
FunbyStudios. (2013, April 6). Ball and Socket [Picture]. Thingiverse. https://www.thingiverse.com/thing:70371
Van den Brand, J. (2021, March 8). U-joint prototype [Video].
List of references
What is Degree of Freedom (DOF) in Mechanics. (2020, November 4). SMLease Design. https://www.smlease.com/entries/mechanism/what-is-degree-of-freedom-dof-in-mechanics/
Types of Kinematic Joints in the Design of Machines. (2008, September 6). Bright Hub Engineering. https://www.brighthubengineering.com/machine-design/6577-types-of-kinematic-joints/
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