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By means of Jody Muelaner, Ph.D. CEng MIMechE

BriefBike is an e-bike designed to fold in one, virtually rapid movement, similar to an umbrella. It is a nice case find out about in mechanism design because of the numerous constraints that will have to all be thought to be to make sure the motorcycle plays accurately when being ridden and folded and when in its folded state. I’ve written ahead of about how the constraint-based comic strip equipment in SolidWorks can be utilized to resolve some slightly easy mechanism synthesis issues. On this article, I display how those ways can also be prolonged, the usage of scripting and information filtering, to resolve a extremely complicated mechanism design problem.

BriefBike used to be designed to fold as temporarily and simply as an umbrella, however the preliminary design used to be a bit of too vast, and there have been problems with the way in which the peak of the seat used to be adjusted. This paintings optimized the mechanism to supply a extra compact fold with enhanced driving geometry.

In a prior article, I offered how geometric constraint-based sketching can synthesize mechanisms. This text takes the guidelines additional, offering a real-world instance of optimizing a mechanism with many various constraints. Maximum particularly, it displays that it turns into not possible to formulate a unmarried comic strip that may surround some of these constraints to without delay resolve for the optimal resolution.

The process, subsequently, best makes use of the geometric constraint comic strip to resolve the mechanism for a given parameter set. This can also be repeated again and again for various mixtures of enter parameters, recording output parameters for each and every configuration. All of the effects can then be indexed in a spreadsheet, filtered to take away configurations that don’t meet crucial standards, and looked after to search out the optimal design. The use of a spreadsheet at this level additionally permits metrics to be calculated to mix parameters, even probably making a unmarried goal serve as that can be utilized to rank designs the usage of a unmarried metric.

The use of macros to resolve huge numbers of configurations

In apply, updating parameters within the comic strip and recording pushed parameters in a spreadsheet turns into time eating and blunder vulnerable once there are various parameters to replace. For instance, with seven parameters (or components) and simply 3 parameter values (or issue ranges), there are 2,187 configurations. Despite the fact that you have to replace the parameters within the comic strip and file the values in Excel for one configuration in only one minute, it will nonetheless take every week of tedious paintings. The use of Excel-driven configurations in SolidWorks might look like the most obvious resolution, however in apply, this doesn’t paintings neatly for an excessively huge collection of configurations. The answer is the use the SolidWorks API to open the document, learn within the parameter set, rebuild the style, and retailer the effects. We created an software to try this, which makes use of 3 easy textual content recordsdata for inputs and outputs:

• Inputs.txt: This document is created via the person to outline the issue to be solved. It has 3 strains:
  • The document identify of the SolidWorks section to open and have interaction with
  • A comma-separated listing of the riding parameters to be up to date via the script
  • A comma-separated listing of the pushed parameters to be recorded via the script
• Parameters.txt: This document could also be created via the person. Every line represents a unique configuration as a comma-separated listing of values, with each and every worth similar to probably the most riding parameters indexed on the second one line in inputs.txt.
• Outputs.txt: This document is created via the script. It has a identical construction to parameters.txt, with each and every line additionally representing a unique configuration as a comma-separated listing of values for each and every parameter. On this case, it’s the pushed parameters indexed at the 3rd line of inputs.txt which are indexed.

The mechanism design procedure comes to first defining the issue in SolidWorks, producing configurations in Energy Question, fixing all configurations the usage of a SolidWorks API script (we’re the usage of an in-house code DimWorker.exe), after which figuring out the optimal resolution via examining the leads to Excel. Experimentation and iteration are more likely to happen at a couple of issues inside this procedure.

Figuring out the limitations

A demonstrator had already been created, which proved the motorcycle may well be opened up in lower than part a moment. On the other hand, it used to be nonetheless a bit of too vast when folded, and optimizing the mechanism to additional scale back the folded width with out impacting the necessary experience traits used to be proving difficult. The huge collection of constraints that had to be concurrently happy intended that an immediate method to to find the optimal mechanism used to be no longer imaginable. This system of the usage of a script to generate a couple of answers used to be subsequently created.

The important thing standards for BriefBike can also be summarized as follows:

• Folds and unfolds in one easy movement right into a curler case structure
  • Not up to 500 mm vast, in a position to roll in the back of an individual thru doorways and crowds, and have compatibility second-stage baggage fold
  • Roughly 1,100 mm in top, offering proper grip top for rolling alongside
  • Not up to 150 mm thick to comfortably retailer flat in opposition to a wall and be held tight in opposition to the frame when in confined areas
  • Transmission angles will have to be more than 30° so the linkage does no longer bind
• 2d level fold that reduces the peak to below 700 mm to be inside the usual baggage measurement for trains across the world (700 x 500 x 300 mm)
• Solid two-wheeled trailing-link design when in curler case structure, defined under
• Driving geometry will have to be related with a standard bicycle. A very powerful parameters are the top attitude, path, wheelbase, place of the ground bracket between the wheels, and efficient stem period. Those parameters are illustrated the place the parametric sketches are outlined later on this article.
• The body will have to be structurally environment friendly. Dimensions measured at the comic strip can be utilized as inputs to loose frame diagram calculations for truss joint forces on the Excel level.
• Portions will have to no longer conflict with each and every different all the way through the folding procedure, and quite a lot of clearance dimensions with the defining sketches mirror this requirement.

What I imply via a solid two-wheeled trailing-link curler case structure can also be simply understood via making an allowance for the 2 various kinds of curler circumstances frequently to be had. First, there may be the four-wheeled selection that you just push in entrance of you. The 4 wheels shape a somewhat solid base and roll alongside fantastic on clean surfaces. On the other hand, if the skin is tough or you need to damage right into a run, the small base and top heart of gravity imply they tip over simply. After which there are the two-wheeled curler circumstances that drag in the back of you. On this case, the bottom bureaucracy a solid tripod between the wheels and your hand. Despite the fact that you all of sudden boost up or run the case directly right into a curb, the wheels elevate off the bottom and land once more in a solid place, and there may be nearly no tendency to tip over. Whilst many folding motorcycles come with wheels that let them to be moved like a four-wheeled case, BriefBike is designed to be pulled alongside like a two-wheeled case.

BriefBike used to be designed to have a large two-wheeled base that may be simply dragged in the back of you. That is rather in contrast to present folding motorcycles, which might be extra just like the a lot much less solid four-wheeled curler circumstances. Even if they’re driven on two wheels, they carry out in the similar volatile means as a result of they’re slim and driven in entrance of you. Just a flat, vast wheelbase dragged in the back of you supplies steadiness required to transport at pace over tough surfaces when the propulsive pressure supplied via your hand is implemented at a top means above the wheels.

The riding parameters outline the mechanism the usage of two sketches. First, a comic strip defines the experience geometry the usage of ten parameters, together with the wheelbase, path, head attitude, achieve, and crank period. The top attitude is pushed via a linear size, as inputting angles the usage of the API proved tougher.

The RideGeom comic strip outlined the necessary parameters affecting the dealing with of the motorcycle. This used to be then used as a reference for the LinkSynth comic strip, which solves for the linkages that permit the motorcycle to fold.

The second one comic strip is the person who if truth be told solves the mechanism synthesis downside. It achieves this via drawing the mechanism within the folded and opened up positions, defining positive key parameters however permitting the constraint-based solver to decide hyperlink lengths and joint positions to succeed in the specified movement. Quite a lot of trial-and-error experimentation used to be required to discover a tough means of constraining this comic strip with dimensions that allowed many various configurations to be examined with out the comic strip failing to resolve.

The LinkSynth comic strip is the place all the mechanism synthesis if truth be told occurs. The primary folding mechanism is a four-bar linkage; the bottom hyperlink isn’t proven. The 3 last hyperlinks are proven within the driving place with a thick dotted line and within the folded place as a thick cast line. Different building, steerage, and envelope geometry are proven with a skinny line. The wheels are best proven within the folded place, and the entrance and rear axles of the body are mated to the RideGeom comic strip, which is hidden on this view. The fastened floor hyperlink is represented via having the joints the place the hyperlinks connect with it coincidentally. The hyperlinks are set to be of equivalent lengths within the two positions, and angles also are compelled to be equivalent via triangulating and atmosphere equivalent period constraints at the diagonals.

The huge collection of parameters within the style implies that even if the usage of automation, parameter ranges will have to be decided on sparingly. If the 16 riding parameters had been each and every given 5 values, there can be 150 billion configurations. With each and every configuration taking about 0.1 seconds to rebuild and retailer the parameters, this is able to take 480 years!

In apply, with better parameter units, reminiscence problems with storing all of the outputs imply the time consistent with configuration can building up dramatically. Even a lot smaller parameter units can subsequently change into unfeasible. So, whilst an automatic optimization permits some distance higher experimentation than you have to hope to succeed in manually, you continue to can’t simply get the pc to check out each imaginable configuration. Subsequently, it’s a good suggestion to begin via manually exploring the parameters to decide which might be maximum delicate after which use the optimization code to discover mixtures of probably attention-grabbing parameter values. This design used to be explored thru six iterations of optimization, with between 1,000 and 40,000 configurations in each and every.

Putting in Excel to generate configurations and filter out effects

After getting decided on a suite of parameters to discover, you will have to generate a desk with all of the mixtures. That is referred to as a complete factorial set within the design of experiments. One of the best ways to try this in Excel is via the usage of Energy Question, any other Microsoft device bundled with Excel. The method comes to connecting tables in an Excel workbook to queries in Energy Question. It is a bit too concerned to give an explanation for totally right here, but it surely’s no longer tricky and is defined neatly on this YouTube video. As soon as Excel has generated the desk of configurations, this can also be copied and pasted into Parameters.txt.

The 18 output-driven parameters had been copied into an Excel desk with the 15 input-driving parameters. An extra 25 columns had been added to calculate different amounts from the parameter values; those integrated clearances between elements and forces calculated at joints. All configurations had been then filtered to make sure enough clearances and establish probably the most fascinating traits, similar to longer wheelbase, steeper head attitude, extra direct transmission angles, decrease joint forces, and a extra compact folded bundle. Those variety standards had been drawn from riding and pushed parameters and values calculated in Excel.

Effects

This mechanism optimization paintings ended in a motorbike with an extended wheelbase, steeper head attitude, and longer path, all leading to a extra solid experience. On the similar time, the body is extra structurally environment friendly, and it folds right into a a lot more compact bundle. You’ll be able to to find out extra about BriefBike at http://www.betterbicycles.org.