I recently heard about an application question related to a light curtain where a small gap existed at the top of the sensing field, between the last beam in the field and the surrounding structure of the machine. There was some concern raised about the gap, and whether or not additional guarding might be needed to close the gap. To answer this question, we need to split it into a few smaller pieces that we can deal with using the tools in the standards.
The first piece to consider is the gap at the top of the sensing field. For this part of the analysis, I’m going to assume that the light curtain is a fixed barrier guard, and we’ll analyse the gap based on that idea.
The second piece of the puzzle is the placement of the light curtain, and we’ll look at that separately. Once we we understand the two pieces, we’ll put them together to see if there are any other issues that may need to be addressed.
The Application
For the purpose of this article, I’ve sketched up the following figures to illustrate the ideas in the article. These drawings don’t represent any actual robot cell or application. Note that the light curtain in the sketch is shown with zero safety distance to the robot envelope. This is NEVER permitted.
Analyzing The Gap
Light curtains are treated the same way that movable guards are treated, so the answer to this question starts with determining the size of the gap. I’m going to reference two sets of standards in answering this question: CSA and ISO.
CSA Z432 2004 [1]  ISO 13857 2008 [2]  

Table 3 – Minimum distance from hazard as a function of barrier opening size  Table 4 – Reaching through Regular openings  
Opening Size (e)  Safety Distance (sr)  Opening Size (e)  Safety Distance (sr) 
11.1– 16.0mm [0.376″–0.625″] 
Slotted >= 89.0 mm [3.5″]Square >= 66 mm [2.6″]  Slot 10 < e <=12Square/Round 10 < e <=12  >= 100 mm>= 80 mm 
49.1–132.0 mm [1.876–5.000″]  Slotted/Square <= 915.0 mm [36.0″]  Slot/Square/Round 40 < e <= 120 mm  <= 850 mm 
The first thing to notice is that CSA and ISO use slightly different opening sizes (e) and safety distances (sr). These differences have their origin in slightly different anthropometric data used to develop the tables. In both cases, the maximum value for e defines the largest opening permitted without additional guarding.
Let’s look at the application to see if the gap between the topmost beam and the edge of the physical guard falls into the bands defined for e.
Based on the sketches of the application, we have a problem: The gap shown above the light curtain is right at the edge of the robot envelope, i.e., the danger zone. We are going to have to either, a) Move the fence back 915 mm to get the necessary safety distance or, b) close the gap off completely, either with hard guarding, or by extending the light curtain to close the gap.
Knowing the size of the gap, we can now decide if the gap should be reduced, or the light curtain moved or enlarged. Since light curtains run about $125/linear inch, adding an additional plate to reduce the size of the gap is likely the most cost effective choice. We also need to know the distance from the topmost beam of the light curtain to the hazard behind the guard. If that distance is less than 915/850 mm, then we have another problem, since the guarding is already too close to the hazard.
Analyzing the Light Curtain
The light curtain positioning is driven by the stopping performance of the machine. Again, let’s reference both CSA and ISO for the relevant calculations.
CSA Z432 2004  ISO 13855 2005 [3] 

5.1 Overall system stopping performance The overall system stopping performance comprises at least two phases.Thetwophasesare linked by Equation (1): T = t_{1} + t_{2} (1) where t_{1} and t_{2} are influenced by various factors, e.g. temperature, switching time of valves, ageing of components. t_{1} and t_{2} are functions of the safeguard and the machine, respectively, and are determined by design and evaluated by measurement. The evaluation of these two values shall include the uncertainties resulting from the measurements, calculations and/or construction. 

Clause 10.11 – Safeguarding device safety distanceThecalculationforminimum safe distance between a safeguarding device and the danger zone of a machine shall be as follows:
S = [K (T_{s} + T_{c} + T_{r} + T_{bm})] + D_{pf} where K = speed constant: 1.6 m/s (63 in/s) minimum, based on the movement being the hand/arm only and the body being stationary. T_{c} = worst stopping time of the control system T_{r} = response time of the safeguarding device, including its interface Note: T_{s} + T_{c} + T_{r} are usually measured by a stoptime measuring device if unknown. T_{bm} = additional stopping time allowed by the brake monitor before it detects stoptime deterioration beyond the end users’ predetermined limits. (For part revolution presses only.) D_{pf} = maximum travel towards the hazard within the presencesensing safeguarding device’s (PSSD) field that may occur before a stop is signaled. Depth penetration factors will change depending on the type of device and application. See Figure 5 for specific values. (If applicable, based on the style of safety device.) 
Clause 6.2.3 – Electrosensitive protective equipment employing active optoelectronic protective devices with a sensor detection capability of ? 40 mm in diameter 6.2.3.1 Calculation The minimum distance, S, in millimetres, from the detection zone to the hazard zone shall not be less than that calculated using Equation (2): S = (K x T ) + C (2) where K = 2 000 mm/s; C = 8 (d – 14), but not less than 0; d is the sensor detection capability of the device, in millimetres (mm). [Author’s Note – T comes from 5.1, above] Then S = (2 000 x T ) + 8(d14) (3) Equation (3) applies to all minimum distances of S up to and including 500 mm. The minimum value of S shall be 100 mm. Where the values for S, calculated using Equation (3), exceed 500 mm, Equation (4) can be used. In this case, the minimum value of S shall be 500 mm. S = (K x T ) + C (2) where K = 1 600 mm/s; C = 8 (d – 14), but not less than 0; d is the sensor detection capability of the device, in millimetres (mm). Then S = (1 600 x T ) + 8(d – 14) Key 1 hazard zone 2 detection zone 3 fixed guard S minimum distance a Direction of approach 
The two calculation methods shown above are essentially the same, with the primary difference being the value of K, the “handspeed constant”. ISO uses a higher value of K for light curtain installations where the field is vertical, or angled as low as 45º. If the calculated value of S is >500 mm, then the value of K is reduced to 1600 mm/s. Using the higher value of K for a North American installation is not wrong, and will result in a more conservative installation result. Use of 1 600 mm/s for machines going into international markets is wrong if S is <500 mm when calculated using 2 000 mm/s.
Let’s assume some values so we can do a representative calculation:
Stopping Time of the system (T) = 265 ms [0.265 s]
Light curtain resolution (d) = 30 mm [1.2″]
Calculating Dpf
Dpf = 8 x (d – 14) = 8 x (30 – 14) = 128
Using K = 2 000 mm/s
S = (2000 x 0.265) + 128 = 658 mm
Since applications where S > 500 mm can be recalculated using K = 1600 mm/s
S = (1 600 x 0.265) + 128 = 552 mm
So, from the above calculation we can see that the distance from the plane of the light curtain to the edge of the robot envelope (i.e., the danger zone) must be at least 552 mm [21.75″]. That distance is enough that some people might be able to stand between the light curtain field and the fixture in the cell, so we should probably add a horizontal light curtain to protect against that possibility. See Figure 7.
Another alternative to adding a horizontal section is to slope the light curtain field, so that the plane of the light curtain is at 45 degrees above the horizontal, with the highest beam as far away from the hazard as possible. See Figure 8. This type of installation avoids the need to replace the existing light curtain, as long as the field depth is enough to meet the calculated Ds.The field could also be laid horizontally, with no vertical component. This will change the Dpf calculation as highlighted by the note in Figure 8. Dpf for a horizontal field is calculated using the following equation:
Dpf = 1 200 mm [48″]
therefore
S = (1 600 x 0.265) + 1200 = 1 624 mm
Note also that there is a height restriction placed on horizontal devices based on the object resolution as well, so the 0.3 m maximum height may not apply to an exclusively horizontal application. Note that ISO 13855 allows H a maximum value of 1 000 mm, rather than cutting the value off at 990 mm as done in CSA Z432. Using either the 14 mm or the 30 mm resolution curtains yields a minimum height of 0 mm and a maximum of 990 mm (CSA) or 1 000 mm (ISO). Note that the 3rd Edition of CSA Z432 is likely to harmonize these distances with the ISO calculations, eliminating these differences.
Also note that field heights where H > 300 mm may require additional safeguards in conjunction with the PresenceSensing Safeguarding Device (PSSD) field.
Going back to our original vertical field installation, there is one more option that could be considered: Reduce the object resolution of the light curtain. If we go down to the smallest object resolution typically available, 14 mm , the calculation looks like this:Dpf = 8 x (1414) = 0
S = (2 000 x 0.265) + 0 = 530 mm
Since S > 500,
S = (1 600 x 0.265) + 0 = 424 mm [16.7″]
While we have substantially reduced the safety distance, it looks like we will still need the horizontal light curtain to ensure that no one can stand behind the curtain without being detected.
If the design of the machinery allows, it might be possible to reduce the stopping time of the machine. If you can reduce the stopping time, you will be able to shorten the safety distance required. Note that the safety distance can never go to zero, and can never be less than that determined by the object resolution applied to the reachingthrough tables. In this case, a 14 mm opening results in an 89 mm [3.5″] minimum safety distance (CSA). Since the stopping time of the machine can never be zero, 89 mm works out to a stopping time of 44.5 ms using K=2 000 mm/s, or 55.6 ms if K= 1 600 mm/s. Very few machines can stop this quickly.
The calculated safety distance is about half of the safety distance required for the gap, at 915 mm. Clearly, closing the gap with the light curtain or hard guarding will be preferable to moving the fence away from the danger zone by 915 mm.
Here’s one more figure to help illustrate these ideas.
Figure 9 shows the difference between the reachingthrough or reachingover light curtain applications. Notice that without a restricting guard above the curtain as we have in our example, the Dpf value goes out to 1 200 mm [48″], rather than the 915 mm value used in our example.
The lower figures show light fence applications, where two or three beams are used, rather than a full coverage light curtain.
Summary
Here are some of the more important considerations:
1) Is the field of the light curtain placed correctly, based on the stopping performance of the machine?
2) What is the object resolution of the sensing field? This dimension may be used to assess the size of the “openings” in the field if this becomes relevant.
3) What is the height of the lowest and highest beams or the edges of the sensing field?
4) What are the dimensions of the gap above the field of the curtain, and the distance from the opening to the closes hazard?
Acknowledgements
I’d like to acknowledge my colleague, Christian Bidner, who suggested the idea for this article based on a realworld application he had seen. Christian works for OMRON/STI in their Toronto office.
References
[1] Safeguarding of Machinery. CSA Z432. Canadian Standards Association (CSA). Toronto. 2004.
[2] Safety of machinery – Safety distances to prevent hazard zones being reached by upper and lower limbs. ISO 13857.International Organization for Standardization (ISO). Geneva. 2008.
[3] Safety of machinery – Positioning of safeguards with respect to the approach speeds of parts of the human body. ISo 13855. International Organization for Standardization (ISO). Geneva. 2010.