9.4: Drivetrain Geometry and Turning


As mentioned above, one of the most common types of robot drivetrain is known as a Skid Steer drivetrain. This type of drivetrain consists of two independent sets of powered wheels, one on each side of its chassis.  By running the sides of the drivetrain at different speeds, it is possible to steer the robot in arcs. This drivetrain is also capable of a zero-radius turn (it will spin in place) if the sides are run at the same speed in opposite directions.

One of the major attributes that defines a drivetrain’s performance is how well it turns. There are two main properties which affect drivetrain turning: Turning Torque and Turning Scrub.

Turning Torque is the torque about the turning point which causes the robot to turn.

Turning Scrub is the friction which resists the robot turning. This is caused by wheels dragging sideways on the ground as the robot turns, resisting the motion of the turn. Turning Scrub is also expressed as a torque about the turning point of the robot, opposing the turning torque.

In a typical skid-steer drivetrain (specifically one in which all the wheels are drive wheels), ALL the wheels will exert force that contributes to the turning torque, and they will ALL drag sideways and contribute to the turning scrub. To help visualize things more simply, one can think of a robot in the odd configuration seen below: 

One can see that Wheel 1 and Wheel 2 contribute to the turning torque.  They each exert a linear force (Force 1 & Force 2) that creates a torque about the turning point.  These wheels do not drag at all as the robot turns, so they don’t contribute to the turning scrub.

Wheel 3 and wheel 4 do not contribute to the turning torque, but they slide sideways as the robot turns and significantly contribute to the turning scrub.  Force 3 and Force 4 are frictional forces from the wheels on the ground; this friction results in the turning scrub.

Now, in a more traditional drivetrain configuration, all the wheels would both contribute to the turning torque, AND the turning scrub: 

In the above case, all four wheels contribute to the Turning Torque, and all four wheels contribute to the Turning Scrub.  Each wheel applies some force that contributes to turning, and each wheel needs to slide sideways and contributes some friction to scrub.

Turning Torque and Turning Scrub are both torques about the robot’s turning point.  As discussed in Unit 7: a torque is a turning force, defined by a linear force at a distance from some center of rotation.  The below diagrams show how the frictional force of the wheel rolling forward contribute turning torque of the robot, and the frictional force of the wheel sliding sideways contributes to the turning scrub of the robot. 

As seen above, the turning torque is contributed to by the friction force of the wheel at a distance from the turning point. 

As seen above, the turning scrub is contributed to by the force of the wheel, around the robot turning point.

If a drivetrain has multiple wheels on the ground, all of these wheels will contribute based on their location in the drivetrain relative to the turning point.


Once one understands the concepts of turning torque, turning scrub, and how they affect robot turning, one can begin to understand how to alter them to make a robot turn more effectively.

How does one reduce turning scrub?

Turning scrub is driven by the force of friction of the wheel sliding sideways on the floor.  By reducing this frictional force, one reduces the turning scrub.  One may also decrease the distance the wheel is from the turning point.

Similarly, one could increase turning torque with the opposite approach; by increasing the frictional force, or increasing the distance from the turning point.

Notice that to decrease turning scrub, one must decrease the wheel friction in the left/right direction. To increase turning torque, one must increase the friction of the wheel in the front/back direction.  It is difficult to modify the friction of a wheel in one direction without affecting the other, so it is usually best to modify the geometry of the robot chassis to help improve robot turning.

However, designers should note that omni-directional wheels have ZERO sideways friction.  This means a drivetrain with an omni-wheel would have NO turning scrub caused by that wheel.  A drivetrain with ALL omni-wheels would have almost ZERO turning scrub!

It is interesting to note that a drivetrain with two omni-wheels and two traction wheels would have a turning point directly between the two traction wheels.  This drivetrain would also have no turning scrub, since the traction wheels would not need to slide sideways. 

The above example shows a drivetrain configuration that is long and narrow. This configuration would likely have poor turning characteristics because of its low turning torque and high turning scrub.

The example above shows a drivetrain configuration that is short and wide. This configuration would likely have very good turning characteristics because of its high turning torque and low turning scrub.

All of the examples discussed so far have been simplified to help illustrate their major underlining concepts.  There is another important consideration that will change the dynamics of these systems – the location of the turning point.  In all the examples seen so far, the turning point has been in the exact center of the robot; this is not always the case.

The turning point will often vary based on the differences between the wheels (front vs. back, or left vs. right).  This is primarily based on the friction between the individual wheels and the floor.  As discussed previously, this friction is dependent on the weight resting on the wheels, and the coefficient of friction of the wheels.  This means that if most of the weight is towards the front of the robot, the turning point would be towards the front.

The traction of the different wheels and the location of the weight of the robot will greatly affect where the turning point is, and will affect the turning torque and turning scrub of the robot.

To recap – in order to make a robot turn better one should primarily adjust three things: the chassis geometry (wide vs narrow, long vs short), the difference in coefficient of friction between the various wheels (primarily front vs back) and the location of the robot’s center of gravity.