Understanding Geometric Motors
If you select points and planes to define the motor, you are creating a geometric motor.
Plane-Plane translation motor—Moves a plane in one rigid body with respect to a plane on another rigid body, keeping one plane parallel to the other. The shortest distance between the two planes measures the position value of the motor. The zero position occurs when the driven and reference planes are coincident.
In addition to the prescribed motion, the driven plane is free to rotate or translate in the reference plane. Thus, a plane-plane motor is less restrictive than a motor on a slider or a cylinder joint. If you want to explicitly tie down the remaining degrees of freedom, specify additional constraints such as a connection or another geometric motor.
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One application of a plane-plane translation motor would be to define a translation between the last link of an open-loop mechanism and ground.
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Plane-Plane rotation motor—Moves a plane in one rigid body at an angle to a plane in another rigid body. During a motion run, the driven plane rotates about a reference direction, with the zero position defined when the driven and reference planes are coincident.
Because the axis of rotation on the driven rigid body remains unspecified, a plane-plane rotation motor is less restrictive than a motor on a pin joint or cylinder joint. Thus, the location of the axis of rotation in the driven rigid body may change in an arbitrary way.
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Plane-plane rotation motors can be used to define rotations around a ball joint. Another application of a plane–plane rotation motor would be to define a rotation between the last rigid body of an open-loop mechanism and ground, such as a front loader.
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Point-Plane translation motor—Moves a point in one rigid body along the normal of a plane in another rigid body. The shortest distance from the point to the plane measures the position value of the motor.
You cannot define the orientation of one rigid body with respect to the other using only a point-plane motor. Also note that the driven point is free to move parallel to the reference plane, and may thus move in a direction unspecified by the motor. Lock these degrees of freedom using another motor or connection. By defining X, Y, and Z components of motion on a point with respect to a plane, you can make a point follow a complex, 3D curve.
Plane-Point translation motor—A plane-point motor is the same as a point-plane motor, except that you define the direction in which a plane moves relative to a point. During a motion run, the driven plane moves in the specified motion direction while staying perpendicular to it. The shortest distance from the point to the plane measures the position value of the motor. At a zero position, the point lies on the plane.
You cannot define the orientation of one rigid body with respect to the other using only a plane-point motor. Also, note that the driven plane is free to move perpendicularly to the specified direction. Lock these degrees of freedom using another motor or connection. By defining X, Y, and Z components of motion on a point with respect to a plane, you can make a point follow a complex, 3D curve.
Point-Point translation motor—Moves a point in one rigid body in a direction specified in another rigid body. The shortest distance measures the position of the driven point to a plane that contains the reference point and is perpendicular to the motion direction. The zero position of a point-point motor occurs when both the reference and driven point lie in a plane whose normal is the motion direction.
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The point-point translation motor is a very loose constraint that must be used carefully to get a predictable motion. You cannot define the orientation of one rigid body with respect to the other using only one point-point motor. In reality, you would need six point-point motors for this.
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Also note that the driven point is free to move perpendicularly to the specified direction, and may do so if you do not specify otherwise. Lock these degrees of freedom using another motor or connection. By defining X, Y, and Z components of motion on a point with respect to a plane, you can make a point follow a complex, 3D curve.