The draw pendulum is a retro specific element used in retractor problems. Based on the three fold repetition of the same position, White can force Black to retract a weak move instead of a strong move. In order to achieve this objective, the critical position must be obtained after Black’s retraction, then White can start the pendulum.
The draw pendulum theme fascinated many composers, who found several ways of expressing it, such as the short form (the so-called amputated draw pendulum), exploiting the losing of castling rights / en passant capture or zugzwang motivated. One major challenge was to show the theme in a five fold presentation – the topic of this post. (Definitions at the end of the article)
Michel Caillaud was the first composer to achieve 5 draw pendulums.
Let’s study together his magnificent composition (H25 from the FIDE Album 2013-2015):
Caillaud, Michel 2nd Prize, feenschach, 2015 In memoriam Milan Velimirović 
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The balance shows that black pawns captured all the 6 missing white pieces. That means no white piece can be uncaptured by black figures during the retro play. Moreover, the black pawn d5 is originally from b7, so it can’t retract on d6. Assuming there will be also an extra black Queen and a black Pawn on a2 – both appearing during the retro play, the white pawns captured four pieces, so White can’t uncapture any other black pieces.
White aims to push back the black King to a square where it can be mated. In order to achieve this objective, White uses the draw pendulum employing alternatively the two black Bishops oscillating between f8 and g7, respectively h5 and g6. The first pendulum is started by a black promotion, while the next by a check given by the black Queen. In the end of each pendulum the weak move – the retraction of the black King – is forced. The systematic manoeuvre repeated 5 times until leads the black King from d3 into the mating net from f6. A monumental conception, which remained unequalled for several years. The first version of this problem appeared in Mat Plus Review, which subsequently ceased its appearance – hence the dedication.
White aims to push back the black King to a square where it can be mated. In order to achieve this objective, White uses the draw pendulum employing alternatively the two black Bishops oscillating between f8 and g7, respectively h5 and g6. The first pendulum is started by a black promotion, while the next by a check given by the black Queen. In the end of each pendulum the weak move – the retraction of the black King – is forced. The systematic manoeuvre repeated 5 times until leads the black King from d3 into the mating net from f6. A monumental conception, which remained unequalled for several years. The first version of this problem appeared in Mat Plus Review, which subsequently ceased its appearance – hence the dedication.
However, in 2019 two composers independently managed to show the same ambitious theme in the fairy retros field.
Thoma, Andreas Die Schwalbe 300/2019 
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Here White wants to force Black to uncapture a white Queen on d6 and place his King on c5. All the draw pendulums involve the black Queen, which occupies the rebirth fields as many times as possible, avoiding the retraction of weak moves. The weak retractions are performed by the black pawns g3 (thrice) and d6 (twice). It is particularly important to note that the introduction of the 4th pendulum decoys the black King to the field where it will be eventually mated. The black King can’t retract his move from c4, because it will be under an illegal check from wPd3. Please note the effective placement of wSc6, hindering the retraction c6:Xd7(>d2). The Høeg type facilitates the uncapture of the desired white Queen. All the white figures are necessary, as the wRd8 is effectively guarding the black King’s rebirth square. Another extraordinary achievement, which hopefully will remain sound.
Crişan, Vlaicu 7th FIDE World Cup, 2019 1st Prize 
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The main plan: 1.S:c2(>Sb1)#?? fails due to the occupation of rebirth square(s). The attempts to free these squares by walking with the white King to South-East: -1.Sh8-f7 e5-e4+ -2.Ke3-f3 Bh2-g1+ -3.Kf2-e3 g4-g3+ -4.Kg1-f2 Bg3-h2+ -5.Sf7-h8 Rh2-h1+ -6.Kf2-g1 Bf4-g3+ -7.Kf1-f2 g3-g2+ -8.Ke2-f1 Rh1-h2+ -9.Kf1-e2 Rh2-h1+ -10.Ke2-f1 Rh1-h2+ -11.Kf1-e2 h2-h1=R+ (forced) -12.Ke2-f1/Kf2-f1 & 1.S:c2(>Sb1)# fail due to the prepared forward defenses: 1…h2# after -4…Bg3-h2+ and 1…Bf2# after -5...Rh2-h1+.
Therefore White needs to employ five consecutive foreplans, each of them using a different draw pendulum. The first foreplan decoys the black Rook oscillating between g5 and f5 to h5. The second foreplan uses the same black Rook oscillating between h5 and h4 and decoys the black Pawn g3 to g4. The third foreplan uses the black Bishop oscillating between g1 and h2 and decoys the black Pawn g2 to g3. The fourth foreplan uses again the black Bishop oscillating between g1 and h2 and forces the unpromotion of the black Bishop g1, hence freeing the white Knight’s rebirth square. The fifth foreplan uses the black Rook between h1 and h2 and forces the unpromotion of the black Rook h1, freeing the white Rook’s rebirth square. The last move also unblocks white Bishop’s rebirth square. The theme is shown in the new German logical style and according to Andrey Frolkin the retro play is perceived as “almost orthodox”.
Therefore White needs to employ five consecutive foreplans, each of them using a different draw pendulum. The first foreplan decoys the black Rook oscillating between g5 and f5 to h5. The second foreplan uses the same black Rook oscillating between h5 and h4 and decoys the black Pawn g3 to g4. The third foreplan uses the black Bishop oscillating between g1 and h2 and decoys the black Pawn g2 to g3. The fourth foreplan uses again the black Bishop oscillating between g1 and h2 and forces the unpromotion of the black Bishop g1, hence freeing the white Knight’s rebirth square. The fifth foreplan uses the black Rook between h1 and h2 and forces the unpromotion of the black Rook h1, freeing the white Rook’s rebirth square. The last move also unblocks white Bishop’s rebirth square. The theme is shown in the new German logical style and according to Andrey Frolkin the retro play is perceived as “almost orthodox”.
I hope this survey will inspire other composers to create retractors showing 5 (or more!) draw pendulums.
Definitions:
Proca Retractor definition:
A Proca Retractor is a defensive Retractor. Black is defending by trying to retract the moves that will forbid (or delay) the achievement of White's goal. You may see at the Retro Corner an example by W. Dittmann of orthodox Proca Retractor showing two en passant captures.
Høeg Retractor :
After any retraction by White or Black, the other side may decide that the retracted move has been a capture, and decide which piece will be resurrected. Of course, legality must be preserved at all times. You may see at the Retro Corner an example by Niels Høeg with many variations.
Anticirce: the capturing piece disappears and is immediately reborn on its home square while the captured piece is removed for good. The capture is not legal if the rebirth square is not free. A pawn capturing on the eighth rank is first promoted and then reborn on the home square of the promoted man. Here "checks are fairy" i.e. a King is not in check if its "capture" is not legal because the rebirth is not possible.
In AntiCirce Cheylan a piece is not allowed to capture on its home square; in AntiCirce Calvet this is allowed.
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