Daniel Fritzinger
Senior Design Engineer
Dana Towing Group
Dana Corp.
Albion, Ind.
Edited by Kenneth Korane




For fairly simple, lowperformance vehicles such as gocarts, golf carts, toy cars, and wagons, designers often choose between single and double, fourbar linkages for the steering system. (See Designing a better steering system, Sept. 26, 1996, and How to design a double fourbar steering system, Dec. 9. 1999, MACHINE DESIGN.)
The rackandpinion design provides another option. As with any steering system, the designer's goal is to have all four wheels pivot about the same turning point. In more analytical terms, when the vehicle is turning, centerlines drawn through both front axles must intersect a line extending through the rearaxle centerline at the same point.
One steering arrangement often used in rackandpinion designs restricts movement of the tie rod to only one axis — left and right. The tie rod cannot move through an arc as in fourbar linkages, so the spindle lever arm usually has slots that permit sliding motion between the tie rod and spindle lever.
Mechanism analysis
In this type of system, the designer typically defines the centertocenter length of the tie rod, T; centertocenter distance between the front axle pivots, D; distance between the tierod centerline and the frontaxle pivot centerline, P; and the distance between front and rear axle centerlines, M. For this application the designer must also define x, the linear sidetoside movement of the tie rod that turns the vehicle.
Let's assume that the tie rod moves to the right, causing the vehicle to turn right. First calculate^{1}^{, }the angle between the spindle lever and front axle. Also assume this value is the same for both the left and rightspindle assemblies.
^{1 }= tan ^{1 }(((DT) / 2) / P) + 90°.
Next, calculate the vehicle's turning radius at the rearaxle center. In actual practice the designer should determine two turning radii, one based on the geometry of the inner steering assembly, the other based on the outer steering assembly. In a properly designed steering system, the length of the vehicle's turning radius calculated for the inner steering assembly will equal the length of the turning radius calculated for the outer steering assembly. In other words, the inner and outer assemblies will both cause the vehicle to assume the same turning radius. All wheels are in harmony and a smooth turn results.
Let's first work with the inner steering assembly. Calculate 2 and 3 after the tie rod moves a distance x to the right.
^{2 }= tan ^{1 }((((DT) / 2) x) / P) + 90°
and
^{3 }= 1 2.
Next solve for the distance between the turningradius pivot point and the inner spindle lever, Hi, which along with Mand 3 form a right triangle.
Hi = M / tan 3.
Finally, solve for Ri, the turning radius based on the inner steering assembly,
Ri = 0.5D + Hi.
Outer steering assembly
To ensure proper steering design, perform the same series of calculations for the outer steering assembly. First determine 4 and 5 after the tie rod moves a distance x to the right.
^{4 }= 90° tan ^{1 }((((TD) / 2) x) /P)
and
^{5 }= 4 1.
Next solve for Ho, the distance between the turningradius pivot point and the outer spindle lever.
Ho = M / tan 5.
Finally, solve for the turning radius based on the outer steering assembly,
Ro = Ho 0.5D.
The inner and outer turning radii will be equal for a properly designed steering system. Use a computer program to speed the design process and verify that the difference between the two turning radii is at or near zero. In addition, recommended practice is to graphically verify the design as a final check.
Articles and computer programs
Previous articles in MACHINE DESIGN on steering geometry include Designing a better steering system, which deals with single, fourbar linkages and How to design a double fourbar steering system. These articles can be found at www.machinedesign2.com/turnstyle.php?ID=44 www.machinedesign2.com/turnstyle.php?ID=45
In addition, the author has written Microsoft Excel computer programs for each type of steering mechanism. The rackandpinion program, for instance, performs all the required calculations, based on user inputs, and compares inner and outer turning radii to ensure a properly designed system. Request a copy via email at [email protected]