Direct torque path differential having spiderless pinions

A differential, comprising:

• an input gear;
• a carrier fixedly connected to the input gear and configured to rotate together with the input gear about a primary axis, the carrier having an internal annular surface with a plurality of cups formed therein and equally spaced apart around a circumference of the carrier;
• a first side gear disposed inside the carrier and configured to rotate about the primary axis;
• a second side gear disposed in the carrier at an end opposite the first side gear and also configured to rotate about the primary axis;
• a side pinion having a body having a flat bottom and a flat top located at an end opposite the flat bottom, the side pinion disposed within each of the plurality of cups and intermeshed with both of the first and second side gears, the side pinion having a plurality of gear teeth that protrude from an associated one of the plurality of cups radially inward toward the primary axis, and an arcuate outer surface connected to the plurality of gear teeth at an axial transition region and conforming to an inner contour of the plurality of cups;
• wherein the arcuate outer surface is formed by rotating a polynomial curve of third order or higher around an axis of the side pinion.

A drivetrain for a mobile machine having first and second traction devices located at opposing sides, the drivetrain comprising:

• a power source;
• a transmission driven by the power source;
• a main pinion operatively connected to an output of the transmission;
• a first half-shaft connected to the first traction device;
• a second half-shaft connected to the second traction device;
• and
• a differential driven by the main pinion to rotate the first and second half-shafts with substantially equal torque, the differential including:
• an input gear intermeshed with the main pinion;
• a carrier fixedly connected to the input gear and configured to rotate together with the input gear about a primary axis, the carrier having an internal annular surface with a plurality of cups formed therein and equally spaced apart around a circumference of the carrier;
• a first side gear disposed inside the carrier and having external teeth at an inner end and an outer end connected to the first half-shaft;
• a second side gear disposed inside the carrier and having external teeth at an inner end and an outer end connected to the second half-shaft;
• and
• a side pinion disposed within each of the plurality of cups and intermeshed with the external teeth of both of the first and second side gears, the side pinion having a plurality of gear teeth that protrude from an associated one of the plurality of cups radially inward toward the primary axis, and an arcuate outer surface connected to the plurality of gear teeth at an axial transition region and conforming to an inner contour of the plurality of cups,
• wherein:
• the arcuate outer surface of the side pinion is formed by rotating a polynomial curve of third order or higher around an axis of the side pinion;
• when the first and second side gears engage the plurality of gear teeth at opposing sides of the side pinion, a reaction force is created;
• and
• the polynomial curve is selected such that a gradient of the arcuate outer surface at an application point of the reaction force is about aligned with the reaction force.