For manipulator robots, there are a few common terms – simple terms – that you should know.  A link makes up the ‘skeleton’ of the robot, and these are connected by joints.  This is exactly like how your arm is made up of the base joint (shoulder) and is connected by a link to another joint (elbow), yet again connected to the final joint (wrist) via another link.  

We Simplify Things

In many undergraduate courses, it is likely that the links will be treated as rigid bodies.  All this means is that it is assumed that the links are infinitely stiff – an applied load will result in zero deflection.  This simplifies solving the math and physics underpinning the operation of the robotic manipulator.  Of course, in real life, robot arms will have some compliance – meaning that they will flex and bend, even if they are made of a stiff material such as a carbon composite or steel.  And when you start to examine robots that move at high speeds or carry heavy payloads, the rigid body assumption would not be accurate enough – but for now, everything is assumed rigid.  

Joints and Degrees of Freedom

A joint provides some connection between the links.  It also usually restricts the motion in some way.  We need to be able to talk about how joints move, and so we introduce the term degrees of freedom (DOF).  It basically means how ‘free’ is the joint to move – and there are six possible ways any single joint can move.  The first three degrees of freedom 1, 2, and 3 – are translational degrees of freedom.  Translational just means moving in a straight line in the cartesian system (X, Y, Z).  In you hold your hand out in front of you, how many directions can you move it in (without bending your wrist)?  One of your options is to move it forward and backward (away from your body/closer to you body).  Note that this is only considered one degree of freedom, since you’re moving it along a single direction (doesn’t matter that it’s both forward and reverse along that direction).  You can also easily move it side to side, or up and down.  You could label any of these directions X, Y, or Z.  If you move it diagonally, that’s just some combination of the X, Y, and Z directions.  So there are three translational degrees of freedom.  There are also three rotational degrees of freedom.  You can rotate your hand side to side, up and down, or roll your arm along its axis – three different rotations about the X, Y, and Z axes.  Just like any position can be reached with the three translational degrees of freedom, any arbitrary rotation can be achieved with these three rotational degrees of freedom.  Adding it all up: the maximum number of DOF for any single joint is six (6).

 

Most joints don’t have six degrees of freedom.  It would be too difficult to make a joint like that, and it would also be difficult to analyze – which is important (keep it simple).  Ultimately it’s just not necessary, because if you combine many simple joints you can easily achieve five or six degrees of freedom, and there are other advantages to having multiple joints (try to imagine have a shoulder joint with all six degrees of freedom, and then no other joints in your arm – it would be far less useful than our current arms).  Most common joints just have one degree of freedom.  A revolute joint (like a door hinge) only allows for a single DOF – rotation about one axis.  A prismatic joint allows for a single translational DOF – like a part with a square hole sliding along a rectangle bar.  A cylindrical joint allows for sliding (like sliding one cylinder within another) and it can also rotate around the axis that it slides.  A spherical joint has 3 degrees of freedom, all rotational, and is very common in our world (although not as common in robotics manipulators).  It is used extensively in suspension systems, to attach suspension links together – like attaching a control arm to the steering knuckle.  It can rotate in any direction.

 

Degrees of Freedom and the End Effector

For manipulators, the two most common joints are by far the revolute and prismatic joints, since these are both simple one DOF joints that allow for rotation and translation, respectively.  By using these joints in a variety of configurations, and in succession, you can build a robot whose end effector (the robot’s ‘hand’) has multiple degrees of freedom.  It is really the DOF of the end effector that matters, and a single joint does not indicate how many DOF the end effector will have.  When you rotate your shoulder, you can raise your hand.  All you’ve done is move your shoulder in one rotational DOF, but your hand (the end effector) has moved both vertically and horizontally.  And so while it may not seem to be immediately intuitive, revolute joints are used more extensively than prismatic joints to move the end effector in the X, Y, and Z directions, partially because it is much faster and easier to rotate than to extend.  Just think of how your arm is built.  There are no translational (prismatic joints), just rotational, but you can move your hand quickly in all translational DOF.  Your wrist is what allows your hand to rotate, but it doesn’t provide any translational ability.  Robot manipulators are set up in much the same way.  Turns out evolution provided us with a pretty cleverly designed robot manipulator.