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Important formulas in kinematics define the velocity and acceleration of points in a moving body as they trace trajectories in three-dimensional space. This is particularly important for the center of mass of a body, which is used to derive equations of motion using either Newton's second law or Lagrange's equations .
In classical mechanics, a kinematic pair is a connection between two physical objects that imposes constraints on their relative movement ().German engineer Franz Reuleaux introduced the kinematic pair as a new approach to the study of machines [1] that provided an advance over the notion of elements consisting of simple machines.
Elements of kinematics diagrams include the frame, which is the frame of reference for all the moving components, as well as links (kinematic pairs), and joints. Primary Joints include pins, sliders and other elements that allow pure rotation or pure linear motion. Higher order joints also exist that allow a combination of rotation or linear ...
A prismatic joint is a one-degree-of-freedom kinematic pair [1] which constrains the motion of two bodies to sliding along a common axis, without rotation; for this reason it is often called a slider (as in the slider-crank linkage) or a sliding pair. They are often utilized in hydraulic and pneumatic cylinders. [2]
A common example of a screw is the wrench associated with a force acting on a rigid body. Let P be the point of application of the force F and let P be the vector locating this point in a fixed frame. The wrench W = (F, P × F) is a screw.
From this point of view the kinematics equations can be used in two different ways. The first called forward kinematics uses specified values for the joint parameters to compute the end-effector position and orientation. The second called inverse kinematics uses the position and orientation of the end-effector to compute the joint parameters ...
Kinematic chains of a wide range of complexity are analyzed by equating the kinematics equations of serial chains that form loops within the kinematic chain. These equations are often called loop equations. The complexity (in terms of calculating the forward and inverse kinematics) of the chain is determined by the following factors:
In kinematics, Chasles' theorem, or Mozzi–Chasles' theorem, says that the most general rigid body displacement can be produced by a screw displacement. A direct Euclidean isometry in three dimensions involves a translation and a rotation. The screw displacement representation of the isometry decomposes the translation into two components, one ...
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