Studies of object motions and their relationships to reference frames that may involve the relative motions of other objects, but without regard to cause. Two types of constrained motion in which objects move along constrained trajectories are addressed by kinematics: motion with a constant velocity and motion with constant acceleration. What also distinguishes it from dynamics is that kinematics involves the study of the motion of bodies without reference to mass and force. In physics, Einstein’s theory of special relativity is a theory about the kinematics of objects at high relative speeds. In contrast, his theory of general relativity is one about gravitation, and as such is a dynamical theory. Kinematics is a branch of classical mechanics that acquired its name through the notion of cinématique devised André-Marie Ampère (1776-1836), and found in his book Essai sur la philosophie des sciences (1834). However, it is considered that the founder is Franz Reuleaux (1829-1905) who wrote in his book Kinematics of machinery: outlines of a theory of mechanics that kinematics was “… the study of the geometric representation of motion p. 56).” In biomechanics, it is used the describe the motion or trajectory of systems of linked parts such as the human arm using 3-D motion capture systems in terms of, for example, velocity and acceleration. What is not properly understood when trying to get to grips with kinematics for the first time is the difference between speed between an velocity: one is a scalar quantity concerned with how fast an object is moving (speed) while the other as a vector quantity not only takes speed into consideration, but also the direction an moving object takes. So far, we have considered a rather simplified vision of what constitutes kinematics. In fact, like dynamics, it consists of two opposing approaches: forward and inverse kinematics. In forward (direct or configuration) kinematics, the problem to be resolved is how to compute the position of an end effector (e.g., a hand) on the basis of knowing the individual joint variables (e.g., of the arm) in terms of rotations and translations. To use an analogy, it is like positioning the limbs of Action Man in order to achieve a particular pose. The computation involved is relatively easy based on matrix multiplication. Inverse kinematics is the reverse problem: given the end point of a movement, what do the angles of joints need to be in order to achieve it? Using another analogy, it is like manipulating the strings on a marionette. The problem is complicated by the fact that calculations are based on an articulated figure consisting of a set of rigid segments linked by joints. Thus, a variety of different angles can yield an infinite number of configurations. As a consequence, the inverse kinematics problem becomes the (biomechanical) degrees-of-freedom problem. The problem is further exacerbated by an infinite number of muscle activation patterns such that any movement can in principle have different ‘means to the same end state’ (the equifinality problem). There are various mathematical solutions for tackling the inverse kinematics problem that become more difficult as one goes from 2-D to 3-D reconstruction, one such solution for the latter being the direct linear transformation method. To summarize, forward kinematics amounts to ‘given joint relations for a limb, what is the orientation and position of its end effector’? The question for inverse kinematics boils down: ‘given the position and orientation of the end effector, what are the joint orientations and rotations required to achieve the desired state of the end effector’? Grasping the difference between forward and inverse kinematics via a verbal description is not as optimal as experiencing it with assistance of dynamic visual aids. Doing so, you will learn that ‘parenting’ and ‘children’ * have been assigned rather different meanings in world of resolving the problems posed by kinematics.
See Acceleration, Basal ganglia (functions), Biomechanical degrees-of-freedom, Biomechanics, Correspondence problem, Degrees-of-freedom (or Bernstein’s) problem, Dynamics, Equifinality, Force, Kinesiology, Kinetics, Mass, Movement (or motor) coordination, Newtonian (or classical) mechanics, Torque, Velocity
* In the world of robotics and computer animations, parenting involves assigning or parenting a (parent or controlling) object to another (child) object. These relationships can be nested to any degree such one or more objects (e.g., joints) are the children of another object, which in turn is the child of yet another. The direction of control can, of course, be in the other direction, thus from child to parent.