Designers at mark Systems Incorporated ran into a vexing mechanical design problem which involved moving a lens into and out of an optical plane. They suggested a number of possible solutions, none of which satisfied the project engineer. The author of this case study was called in as a consultant; details of the problem and of his solution to it are documented on the following pages.

Mark Systems Incorporated is a young Santa Clara company whose principal business has been the manufacture of portable film processing equipment. In order to insure the company's continuing existence and growth, the management of Mark Systems has been eager to develop other products.

Early in 1966 MSI management learned of a unique engineering concept which solved in principle a difficult problem in the field of optical equipment. A good, practical conversion of this solution to functioning hardware would be of great interest to both civilian and military users. The marketing people at MSI conducted a survey intended to gauge the total market. Their estimates of the total market potential were so great that even after allowing for normal "Salesman's Enthusiasm" MSI management felt justified in making the decision to develop a working model for demonstration purposes.

The device chosen to demonstrate the basic concept was a special binocular; it was a relatively crude device, but sufficed to show that the basic idea was a good one. Proof of the effectiveness of the demonstrator was provided by the fact that MSI began receiving orders for production units. Undoubtedly, among the users of the production unit would be sportsmen and military people holding the device in their hands while working under adverse field conditions.

A group of MSI designers was assigned the task of developing from the demonstrating model a design suitable for production; they quickly ran into several nasty mechanical design problems. One of these was the problem of miving a lens into and out of an optical train by the use of the left thumb or a finger squeeze of the left han, possibly while wearing heavy gloves ( see Exhibit 1 for a visualization of thisproblem). The project engineer for this problem was young, aggressive, creative, and not easily pleased with marginal solutions. His designers offered slotted links, cable drives, bell cranks, spur and bevel gear trains, and cams (see Exhibits 1, 2, 3), but none of these satisfied him. His objections were that there were too many pieces (expensive); or too much friction and weight (a military man, for example, would throw the device away if it were difficult to use); or too delicate or not positive (reliability is important!). He kept reminding his designers of the design criteria he had established for this particular problem.

The mechanism had to :

1. have as few parts as possible
2. be light weight and compact
3. be positive in its action
4. be smooth acting and free of jamming (easily operable to avoid operator fatigue)
5. be relatively insensitive to shock
6. be inexpensive to fabricate
7. have as little wear as possible

The designers replied that after all the ideas they had discussed, there didn't seem to be anything else to try. With an eye on his schedule and budget, the project engineer decided to invest in some outside consulting help from the author of this case history. The decision was based on the fact that the author had participated in the very early work on the demonstrator and was not new to its problems. Also, all of the designers knew him and would accept him readily. Twenty working hours were allowed to present a feasibly concept. The author listened to the story and commented, "Unfortunately, I can agree with all of you. None of the proposed solutions looks good, but what else is there to try?" The project engineer's answer was, "Dont't ask us, you're being paid to tell us what else there is to try." After an embarassing silence, the author said, "Wait a minute. I'm not certain, but there may be something. I remember a mechanism called space crank - some of the modern text books on kinematics describe it, and if my memory serves me correctly there was an article in a trade journal some time ago which discussed this mechanism. I've never used it before but I think it holds a lot of promise for your application. I'll look through my file of old magazine articles to see if I can find something on it." The search did turn up an article on the subject of space cranks. From the description, it seemed to fit the operating and fabricating requirements quite well. For example, given a uniform input, the linkage output characteristics (displacement, velocity and accelaration) were quite smooth and free of discontinuities. This indicated smooth action which would be free of jamming. The displacement curve, in particular, displayed a very interesting and desirable shape; in the region of extreme angular displacement this curve became quite flat in a manner somewhat like a "dwell". This in turn meant that it would not be necessary to develop a precise input motion in order to achieve a reasonably precise output motion. Furthermore, in this dwell condition the linkage formed a natural positive acting detent, i.e., it could not be driven by its load. Also, the manufacture of links joined by pins is relatively simple and inexpensive (especially inexpensive when considering production quantities which might number in the thousands. In terms of cost the closest competitor would be catalog gears, but even they would cost more than the links). It seemed as though the links could be small (i.e., light) and yet rugged (i.e., dependable and insensitive to shock). For these reasons a layout was prepared which showed that the space linkage approach was indeed feasible as well as attractive from a functional and manufacturing point of view.

However, in order to build a prototype of the space crank so that its performance could be verified, it was necessary to establish the values of the angles which enter into the design equations (see Exhibit 4). Inasmuch as the desired maximum output angle was known (Ø max = 900) and the maximum output angle is a simple function of the angle called gamma (Ø max = 2 gamma), part of the problem was already solved. The design equations show, however, that the angle lambda influences the displacement, velocity, and acceleration characterisitics of the crank output. The details of this influence were not immediately obvious to the author from an examination of the equations. In addition, some constraint on the range of permissible values was inherent in the space available (see Exhibit 5). This was especially important because of the dwell characteristic of the displacement curves in the region of maximum output angle. The available information indicated that a desirable displacement characteristic could be achieved by using small values for the angle lambda; but this information was insufficient for a design decision on a production model.

Somehow the author had to investigate this aspect of the crank design in order to develop a "feeling" for how it would behave. There was nothing available in what remained of his original twenty hours except to attempt a manual solution of the equations for several representative values of lambda and gamma. The calculations were done with a aid of a desk - top calculator (how welcome a computer would have been !).

On the basis of these calculations (and the curves plotted from them), the published curves in the available literature, and the space available in the actual product, values of gamma and lambda were adopted for the production model and the detailed design was started. As of this date, March 1968, the production drawings are almost ready for release.