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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]
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.
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.
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]
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.
The robot Jacobian results in a set of linear equations that relate the joint rates to the six-vector formed from the angular and linear velocity of the end-effector, known as a twist. Specifying the joint rates yields the end-effector twist directly. The inverse velocity problem seeks the joint rates that provide a specified end-effector twist.
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.
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.