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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]
For each joint of the kinematic chain, an origin point q and an axis of action are selected for the zero configuration, using the coordinate frame of the base. In the case of a prismatic joint, the axis of action v is the vector along which the joint extends; in the case of a revolute joint, the axis of action ω the vector normal to the rotation.
Line representations in robotics are used for the following: They model joint axes: a revolute joint makes any connected rigid body rotate about the line of its axis; a prismatic joint makes the connected rigid body translate along its axis line. They model edges of the polyhedral objects used in many task planners or sensor processing modules.
A slider-crank linkage is a four-bar linkage with three revolute joints and one prismatic, or sliding, joint. The rotation of the crank drives the linear movement the slider, or the expansion of gases against a sliding piston in a cylinder can drive the rotation of the crank.
A prismatic joint can be formed with a polygonal cross-section to resist rotation. The relative position of two bodies connected by a prismatic joint is defined by the amount of linear slide of one relative to the other one. This one parameter movement identifies this joint as a one degree of freedom kinematic pair. [2]
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.
The first industrial robot, [1] Unimate, was invented in the 1950s. Its control axes correspond to a spherical coordinate system, with RRP joint topology composed of two revolute R joints in series with a prismatic P joint. Most industrial robots today are articulated robots composed of a serial chain of revolute R joints RRRRRR.
The system of six joint axes S i and five common normal lines A i,i+1 form the kinematic skeleton of the typical six degree-of-freedom serial robot. Denavit and Hartenberg introduced the convention that z-coordinate axes are assigned to the joint axes S i and x-coordinate axes are assigned to the common normals A i,i+1.