This means there are an infinite number of ways in which your arm can move to place your hand at a specific location on the table.įortunately, our brains are designed to determine the “best” solution when we need to do something like pick up an object. If you place your hand on a table, you can change the position of your wrist and shoulder without changing the position of your hand. And although some robot designs can have seven or more axes of motion, it’s important to note that a robot with more than six axes of motion is kinematically redundant - meaning it can reach a given position from multiple joint states.Ī good example of a kinematically redundant system is the human arm. In robot lexicon, “degrees of freedom” often refers to the number of robot joints or axes of motion. We established earlier that only six degrees of freedom (three translational and three rotational) exist in three-dimensional space, but it’s not uncommon to hear of a robot with seven or more “degrees of freedom.” So how can a robot have more than six degrees of freedom? Motions in the constrained degrees of freedom represent planar and angular errors.Ĭan robots have more than six degrees of freedom? These motions due to deflection in the constrained degrees of freedom are planar and angular errors. And offset, or moment, loads applied to the bearing can cause it to rotate slightly around any of the three axes. 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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