In human movement analysis, the last link of an open kinematic chain, typically the hand or the foot, needs to be positioned in a specified place with a specific orientation. This link is termed the end effector. This concept is very similar to end effector robots that use robotics to position the arms at a specified 3D position and orientation. One of the hardest concepts to understand in biomechanics of human movement is the fact that the body utilizes only angular joint DOF kinematics to produce what seem to be translational motions of the end effector. So even though we observe a sprinter translating down the track, that motion is purely the result of a well coordinated sequence of joint rotations starting from the core.Same for a basketball player jumping straight up to grab a rebound, which is caused through a well coordinated sequence of joint rotations starting from the core resulting in the player jumping 42″ vertically off the ground. Most observers note the athlete moving straight down the track or jumping straight in the air. To them that implies the vertical and horizontal forces on the ground cause the resultant motion. What they miss is the angular kinematics of the human body that are required to create the internal joint torques (moments) and forces that cause the resultant action-reaction with the floor or ground which ultimately catapults the athlete in the desired direction. The ground reaction is what causes the change in direction. But the power to cause that was already set in motion by the core of the human body; the ground just provides a temporary constraint on the motion.
Mark Verstegen does a great job discussing end effector mobility in his book Core Performance: “We have a tendency to think of movement as starting from the limbs. If we reach out to grab something or step forward, we think of those motions as originating with the end result – we’ve reached out; therefore, we’ve used our arms. We’ve stepped forward, so we’ve worked our legs…Movement, however, starts from the very center of the body, the core area of the torso.”
One consideration when examining end effector mobility is the fact that the human arm has 7 degrees of freedom (DOF). An example of an upper extremity model featuring realistic pronation and supination by Dr. Gary Yamaguchi from Dynamic Modeling of Musculoskeletal Motion is shown below.
A rigid body in 3D space needs just 6 DOF to fully describe its position and orientation. Because the human arm has 7 DOF, there is essentially an extra DOF when analyzing end effector mobility. Suppose that we want to model grabbing an object in 3D space; for example grabbing a light bulb, picking an apple off of a tree, catching a baseball, etc. Given the same starting point of the shoulder joint origin, there are a number of different solutions to solving that problem because the arm has 7 DOF. Another way to look at this is to place your hand on a desk and not move it; while also keeping the shoulder center in the same location. Despite these motion constraints at the hand and shoulder, we still have some ability to move the elbow. Again, this is due to the fact that the arm has an extra DOF when looking at end effector mobility scenarios.