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The following example shows a typical multibody system. It is usually denoted as slider-crank mechanism. The mechanism is used to transform rotational motion into translational motion by means of a rotating driving beam, a connection rod and a sliding body. In the present example, a flexible body is used for the connection rod.
The movement of a body, or link, is studied using geometry so the link is considered to be rigid. [1] The connections between links are modeled as providing ideal movement, pure rotation or sliding for example, and are called joints. A linkage modeled as a network of rigid links and ideal joints is called a kinematic chain.
These figures show a single linkage in the fully extended, mid-stride, retracted, and lifted positions of the walking cycle. These four figures show the crank (rightmost link in the first figure on the left with the extended pin) in the 0, 90, 180, and 270 degree positions. This animation shows the working of a klann mechanism.
The principle of virtual work yields a set of linear equations that relate the resultant force-torque six vector, called a wrench, that acts on the end-effector to the joint torques of the robot. If the end-effector wrench is known, then a direct calculation yields the joint torques.
One of the links is the ground or base. [1] This configuration is also called a pantograph, [2] [3] however, it is not to be confused with the parallelogram-copying linkage pantograph. The linkage can be a one-degree-of-freedom mechanism if two gears are attached to two links and are meshed together, forming a geared five-bar mechanism. [1]
If the links in the system move planes parallel to a fixed plane, or in concentric spheres about a fixed point, then the mobility formula is = + =. If a system of links and joints has mobility M = 0 or less, yet still moves, then it is called an overconstrained mechanism.
A typical redundant manipulator has seven joints, for example three at the shoulder, one elbow joint and three at the wrist. This manipulator can move its elbow around a circle while it maintains a specific position and orientation of its end-effector. A snake robot has many more than six degrees of freedom and is often called hyper-redundant.
The JPL mobile robot ATHLETE is a platform with six serial chain legs ending in wheels. The arms, fingers, and head of the JSC Robonaut are modeled as kinematic chains. The movement of the Boulton & Watt steam engine is studied as a system of rigid bodies connected by joints forming a kinematic chain.