The Design of a Novel Pure-Rolling Transmission to Convert Rotational into Translational Motion

摘要

Contributed by the Mechanisms and Robotics Committee for publication in the JOURNAL OF MECHANICAL DESIGN. Manuscript received October 2000; revised March 2002. Associate Editor: S. K. Agrawal. Rack-and-pinion transmissions are broadly accepted means of power transmission between a rotating motor and a translating load. Their technology is well established within the framework of gearing 1. For decades, this transmission went unchallenged, that is, until the advent of highly accurate manufacturing processes that gave rise to more accurate, smoother, and more reliable alternatives, such as ball screws and linear actuators. In robotics and mechatronics applications, whereby motion is controlled using a piece of software, the conversion of motion from rotational to translational is usually done by alternative means. Of these alternatives, ball screws are gaining popularity, one of their drawbacks being the high number of moving parts that they comprise, for their functioning relies on a number of balls rolling on grooves machined on a shaft; one more drawback of ball screws is their low load-carrying capacity, stemming from the punctual form of contact by means of which loads are transmitted. Linear bearings solve these drawbacks to some extent, for they can be fabricated with roller bearings, their drawback being that these devices rely on a form of direct-drive motor, which makes them expensive to produce and to maintain. Hence the motivation behind the work reported here. Upon considering the foregoing alternatives to rack-and-pinions, along with their drawbacks, we decided to try to replace these transmissions with cam mechanisms. In the methodology that we adopted, only line contact is considered, for this methodology is based on the three-dimensional version of the Aronhold-Kennedy Theorem, as described extensively in 2. Furthermore, the cam mechanisms at the core of the transmissions under disclosure are of the translating roller-follower type. A unified methodology on the synthesis of cam mechanisms was introduced in the foregoing reference. This methodology was exploited extensively to develop the software package USyCaMs 3, which proved an invaluable tool in the design of the transmission reported in this paper. In USyCaMs we introduced a displacement program called cycloidal-modified, which can be varied smoothly from cycloidal to linear motion with the aid of a coefficient that changes from unity to zero. The results obtained with this function motivated us to investigate the possibility of transmitting a linear—in the algebraic sense—displacement program as needed in rack-and-pinions. This methodology has already led to the development of friction-and-backlash-free speed reducers with virtually unlimited stiffness, as reported in 4. The transmission reported in this paper, termed Slide-o-Cam, is currently under development at McGill University's Centre for Intelligent Machines, within a research program aimed at highly accurate transmissions for robotics and mechatronics applications. In the context of this program, we envision applications of Slide-o-Cam as a drive for revolute joints using hydraulic pistons as actuators, for Slide-o-Cam is a reversible transmission. The transmission introduced here, Slide-o-Cam, has the morphology of an indexing cam mechanism (ICM), i.e., a cam mechanism whose follower bears a periodic geometry. The follower pattern repeats itself N times per turn of the cam, the ICM at hand thus being said to have Nstages or indexing steps. An ICM is designed so as to allow the production of a periodic, nonreversing speed of the follower when the cam rotates at a constant angular speed. While Slide-o-Cam stems from the concept of ICM, its distinguishing feature is the type of periodic speed produced on the follower, namely, a translational speed that is proportional to the cam speed. As a matter of fact, Slide-o-Cam is reversible, and hence, can be used to convert the translational motion of a moto