For example, loads placed on the bearing in the downward (Z) or lateral (Y) direction can cause the bearing to deflect in those directions. This is because deflection of the bearing block can introduce small motions in the constrained degrees of freedom. However, just because motion is constrained in the other five degrees of freedom doesn’t mean that there is zero movement in those axes. Therefore, it has only one degree of freedom. The bearing on a linear rail can only move in one direction, with motion in the other two translational axes and three rotational axes constrained. Motions in the other five degrees of freedom - translation along the Y and Z axes and all three rotational motions - are constrained by the guide being mounting to the rail. The bearing has only one degree of freedom, since it can only move along one axis, typically referred to as the X axis. Widnall, Penn State UniversityĪn example of degrees of freedom in linear motion is a bearing block mounted to a profiled linear guide. But to locate a rigid body in three-dimensional space requires six coordinates: X, Y, Z, and the rotational coordinates around each of the three axes. To locate a point mass in three-dimensional space requires only three coordinates: X, Y, and Z. These three translational and three rotational movements define the six degrees of freedom (DoF) of a rigid body in 3D space. But it can also rotate around the X, Y, and Z axes, creating rotational motions referred to as roll, pitch, and yaw, respectively. It can make translational movements forward and back, left and right, and up and down in the X, Y, and Z axes. The classic example of a rigid body in three-dimensional space is an aircraft in flight. The six degrees of freedom (DOF) include three translational motions and three rotational motions. But a rigid body can both move, or translate, along these three axes and rotate about them, so we need three translational (X, Y, and Z) and three rotational coordinates (rotation about X, Y, and Z) to locate its position. If the object is a point mass, we only need three coordinates (X, Y, and Z) to locate its position. To identify the position of an object in three-dimensional space, we use a coordinate system that defines three axes: X, Y, and Z.
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