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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]
The most familiar joints for linkage systems are the revolute, or hinged, joint denoted by an R, and the prismatic, or sliding, joint denoted by a P. Most other joints used for spatial linkages are modeled as combinations of revolute and prismatic joints. For example,
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.
Repeated joints may be summarized by their number; so that joint notation for the SCARA robot can also be written 2RP for example. Joint notation for the parallel Gough-Stewart mechanism is 6-UPS or 6(UPS) indicating that it is composed of six identical serial limbs, each one composed of a universal U, active prismatic P and spherical S joint.
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]
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.
An example of a simple open chain is a serial robot manipulator. These robotic systems are constructed from a series of links connected by six one degree-of-freedom revolute or prismatic joints, so the system has six degrees of freedom. An example of a simple closed chain is the RSSR spatial four-bar linkage.