
657 F.3d 586 (2011)
Herman NELSON, Joel Decatur, Andre Lawson and Ernest Carter, Plaintiffs-Appellants,
v.
Janet NAPOLITANO, Secretary of the Department of Homeland Security, Defendant-Appellee.
No. 10-2260.
United States Court of Appeals, Seventh Circuit.
Argued April 4, 2011.
Decided September 15, 2011.
Gerardo S. Gutierrez (argued), Attorney, Chicago, IL, for Plaintiffs-Appellants.
Gina E. Brock (argued), Attorney, Ann L. Wallace, Attorney, Office of the United States Attorney, Chicago, IL, for Defendant-Appellee.
Before KANNE, ROVNER and SYKES, Circuit Judges.
ROVNER, Circuit Judge.
Herman Nelson, Joel Decatur, Andre Lawson and Ernest Carter were employed by the Department of Homeland Security ("DHS"). In 2007, they filed a six-count employment discrimination suit against DHS.[1] After the district court granted the *587 defendant's motion to dismiss two of the counts, DHS failed to answer the complaint, apparently due to an oversight. In May 2009, the plaintiffs moved for a voluntary dismissal without prejudice, pursuant to Federal Rule of Civil Procedure 41(a)(1)(A). The court granted the motion and struck as moot all other pending matters in the case. Nine months later, the plaintiffs moved to reinstate the case under Federal Rule of Civil Procedure 60(b). The court denied the motion and the plaintiffs appeal. We affirm.

I.
Nelson, Decatur, Lawson and Carter were Federal Air Marshals. They charged DHS with race- and age-based discrimination, as well as retaliation against certain of the plaintiffs who complained about discriminatory practices. Approximately two years after filing the complaint, one of the plaintiffs, Andre Lawson, was arrested for sexual assault. After leaving the Air Marshals, Lawson had become a home detention officer. In that capacity, he made monitoring visits to offenders sentenced to home confinement. Lawson eventually pled guilty to sexually assaulting a woman he was assigned to monitor. After Lawson was arrested but before he pled guilty, the other plaintiffs, fearing the effect of the arrest on the case and uncertain of the outcome of Lawson's criminal proceedings, decided to request the voluntary dismissal of the lawsuit under Rule 41(a)(1)(A). They were under the impression that they could move under Rule 60(b) to reinstate the suit within one year. They anticipated that the criminal matter would be resolved by then and they could evaluate whether to move forward with their suit at that time.
Rule 41 provides for voluntary dismissal of an action under certain circumstances:
a) Voluntary Dismissal. (1) By the Plaintiff. (A) Without a Court Order. Subject to Rules 23(e), 23.1(c), 23.2, and 66 and any applicable federal statute, the plaintiff may dismiss an action without a court order by filing: (i) a notice of dismissal before the opposing party serves either an answer or a motion for summary judgment; or (ii) a stipulation of dismissal signed by all parties who have appeared. (B) Effect. Unless the notice or stipulation states otherwise, the dismissal is without prejudice. But if the plaintiff previously dismissed any federal-or state-court action based on or including the same claim, a notice of dismissal operates as an adjudication on the merits.
Fed.R.Civ.P. 41. As we noted, because of an oversight, DHS had not yet answered the complaint even though a considerable amount of time had passed, and so the plaintiffs were entitled to voluntarily dismiss the suit without leave of court and without a court order, using Rule 41(a)(1)(A)(i). Although the plaintiffs miscaptioned their notice of dismissal as a "Motion for Voluntary Dismissal Pursuant to FRCP 41(a)(1)(A)," that filing effected the immediate dismissal of the suit. Smith v. Potter, 513 F.3d 781, 782 (7th Cir.2008); Jenkins v. Village of Maywood, 506 F.3d 622, 624 (7th Cir.2007). No action remained for the district court to take. Smith, 513 F.3d at 782; Jenkins, 506 F.3d at 624. The court's subsequent order purporting to dismiss the case was therefore void and had no legal effect. Smith, 513 F.3d at 782-83.
A suit that is voluntarily dismissed under Rule 41(a) generally is treated as if it had never been filed. Smith, 513 F.3d at 783; Beck v. Caterpillar, Inc., 50 F.3d 405, 407 (7th Cir.1995). See also Robinson *588 v. Willow Glen Acad., 895 F.2d 1168, 1169 (7th Cir.1990) (the effect of a voluntary dismissal is to turn back the clock; it is as if the plaintiff's lawsuit had never been brought); Szabo Food Serv., Inc. v. Canteen Corp., 823 F.2d 1073, 1078 (7th Cir. 1987) (same); United States v. Mount Vernon Memorial Estates, Inc., 734 F.2d 1230, 1236 (7th Cir.1984) (same). Once an action has been dismissed under Rule 41(a)(1) without prejudice, the plaintiff may bring the suit again by filing a new complaint. Richmond v. Chater, 94 F.3d 263, 267 (7th Cir.1996) (filing a new complaint and paying a new filing fee is generally required following dismissal without prejudice); Adams v. Lever Bros. Co., 874 F.2d 393, 395-96 (7th Cir.1989) (refiling a complaint after a Rule 41(a)(1) dismissal requires a new docket fee and compliance with the statute of limitations); McCallBey v. Franzen, 777 F.2d 1178, 1184 (7th Cir.1985) (Rule 41(a)(1) allows a plaintiff to "dismiss without the court's permission, and without prejudice to his being able to bring a new suit, if the defendant has not yet answered the complaint or moved for summary judgment"); Fed.R.Civ.P. 3 ("A civil action is commenced by filing a complaint with the court.").
But the plaintiffs here did not file a new lawsuit. Instead, nine months after the dismissal, and after the statute of limitations had expired, they filed a "Motion to Reinstate Complaint Pursuant to FRCP 60(b) that was Voluntarily Dismissed Without Prejudice." Without specifying which of the six subparts of Rule 60(b) applied, the plaintiffs explained that they sought voluntary dismissal "following a set of unforeseen circumstances regarding one of the named plaintiffs that had a tendency to directly impact on these proceedings and required additional time to sort out the legal impact to the plaintiffs' case in chief." R. 38, at 2. The plaintiffs maintained that charges against one of them had caught them by surprise, and that they decided for tactical reasons to dismiss the suit until those charges were resolved. They sought "reinstatement" of their complaint and requested a status hearing to set a discovery cut-off date and address pre-trial matters. DHS responded that the court lacked jurisdiction to entertain a Rule 60(b) motion in a case that had been voluntarily dismissed. In the alternative, DHS argued that the plaintiffs had not demonstrated sufficient grounds to warrant relief under Rule 60(b). In reply, the plaintiffs responded that the Rule "is written broadly enough where the Court is free to consider any reason for relief." R. 42, at 4-5.

II.
The district court was uncertain whether it retained jurisdiction to consider the Rule 60(b) motion following a voluntary dismissal under Rule 41(a)(1)(A)(i). Although it is true that a suit that has been voluntarily dismissed under Rule 41(a)(1)(A)(i) generally is treated as if it had never been filed, the Supreme Court and this court have recognized the limits of that characterization. For example, the Supreme Court held that "a federal court may consider collateral issues after an action is no longer pending." Cooter & Gell v. Hartmarx Corp., 496 U.S. 384, 395, 110 S.Ct. 2447, 110 L.Ed.2d 359 (1990). Thus, after a voluntary dismissal under Rule 41(a)(1)(A)(i), a court may still impose sanctions under Federal Rule of Civil Procedure 11, or adjudicate a criminal contempt charge even after the action in which the contempt arose has been terminated. Cooter & Gell, 496 U.S. at 395-96, 110 S.Ct. 2447. The Court noted that the purpose of Rule 41(a)(1) is to limit a plaintiff's ability to dismiss an action. 496 U.S. at 397, 110 S.Ct. 2447. Prior to the promulgation of Rule 41, liberal procedural rules allowed plaintiffs to dismiss as a matter of right until the entry of the verdict. Rule 41(a)(1) preserved a plaintiff's *589 right to dismiss an action without the permission of the court or the agreement of the adverse party only during the (usually) brief period before the defendant answered or moved for summary judgment, before the defendant had made a significant commitment of time and money. Cooter & Gell, 496 U.S. at 397, 110 S.Ct. 2447. "Rule 41(a)(1) was not designed to give a plaintiff any benefit other than the right to take one such dismissal without prejudice." Id. The Court noted that the Rule 41(a)(1) and Rule 11 shared the goal of curbing abuses of the judicial system. Allowing a plaintiff to avoid Rule 11 sanctions by taking a dismissal would eliminate the incentive for litigants to investigate carefully before filing papers. Cooter & Gell, 496 U.S. at 397-98, 110 S.Ct. 2447. The Court therefore concluded that a plaintiff's voluntary dismissal under Rule 41(a)(1) did not divest a district court of jurisdiction to consider a defendant's Rule 11 motion. 496 U.S. at 398, 110 S.Ct. 2447. See also Szabo Food, 823 F.2d at 1077-79 (noting the limits to treating a Rule 41(a)(1) dismissal as if the case had never been brought and holding that courts could award fees under Rule 11 or issue sanctions for contempt of court even if the plaintiff had voluntarily dismissed the suit).
A voluntary dismissal pursuant to Rule 41(a)(1)(A)(i), therefore, does not deprive a district court of jurisdiction for all purposes. Citing McCall-Bey, DHS now concedes that a district court retains jurisdiction to consider a Rule 60(b) motion following a voluntary dismissal. In McCall-Bey, we said:
An unconditional dismissal terminates federal jurisdiction except for the limited purpose of reopening and setting aside the judgment of dismissal within the scope allowed by Rule 60(b).
777 F.2d at 1190. DHS offers the example of a defendant faking his own death with a fraudulent death certificate in order to induce a plaintiff to voluntarily dismiss. In those circumstances, DHS posits that, if all other requirements of Rule 60(b) were met, the district court would be able to grant relief to the plaintiff. We agree that there may be instances where a district court may grant relief under Rule 60(b) to a plaintiff who has voluntarily dismissed the action.

III.
In this case, however, the district court did not abuse its discretion in denying the plaintiffs' Rule 60(b) motion. Relief under Rule 60(b) is an extraordinary remedy granted only in exceptional circumstances. Wickens v. Shell Oil Co., 620 F.3d 747, 759 (7th Cir.2010); Eskridge v. Cook County, 577 F.3d 806, 809 (7th Cir. 2009). We review the district court's decision to deny a Rule 60(b) motion for abuse of discretion. Wickens, 620 F.3d at 758; Eskridge, 577 F.3d at 808-09. Rule 60(b) allows a court to relieve a party from a final judgment, order, or proceeding for the following reasons:
(1) mistake, inadvertence, surprise, or excusable neglect;
(2) newly discovered evidence that, with reasonable diligence, could not have been discovered in time to move for a new trial under Rule 59(b);
(3) fraud (whether previously called intrinsic or extrinsic), misrepresentation, or misconduct by an opposing party;
(4) the judgment is void;
(5) the judgment has been satisfied, released or discharged; it is based on an earlier judgment that has been reversed or vacated; or applying it prospectively is no longer equitable; or
(6) any other reason that justifies relief.
Fed.R.Civ.P. 60(b). The plaintiffs listed all of the subsections of Rule 60(b) in their motion in the district court but did not *590 specify which applied. Instead, they contended that they voluntarily dismissed their suit for equitable and tactical reasons related to their surprise over the arrest of one of the plaintiffs. Because the dismissal was without prejudice, they assumed that they were entitled to reinstatement so long as they moved within the one-year period specified in Rule 60(c). Rule 60(c) provides that all motions under Rule 60(b) must be brought within a reasonable time and, for the first three reasons set forth in the rule, no more than one year from the entry of the judgment or order or the date of the proceeding. Perhaps by citing the one-year limit set forth in Rule 60(c), the plaintiffs meant to signal reliance on one of those first three reasons in Rule 60(b). They failed, however, to set forth any argument or cite any cases supporting relief on any of those grounds. On appeal, the plaintiffs confuse the matter further by claiming that they relied on Rules 60(b)(1), 60(b)(2) and 60(b)(6) in the district court, and that they "could have relied on the language of Rule 60(b)(5)." Appellants' Brief, 11-12. Apparently, they expected the district court to determine which section applied and to manufacture their argument for them. They failed at any point to make a cogent argument for Rule 60(b) relief under any provision, and that was reason enough for the district court to deny the motion. United States v. Thornton, 642 F.3d 599, 606 (7th Cir.2011) (undeveloped and unsupported arguments may be deemed waived); United States v. Dunkel, 927 F.2d 955, 956 (7th Cir.1991) (a skeletal argument does not preserve a claim for appeal). Neither the district court nor this court are obliged to research and construct legal arguments for parties, especially when they are represented by counsel. Judge v. Quinn, 612 F.3d 537, 557 (7th Cir.2010), amended on denial of reh'g, 387 Fed.Appx. 629 (7th Cir.2010), cert. denied, ___ U.S. ___, 131 S.Ct. 2958, 180 L.Ed.2d 245 (2011). The plaintiffs assumed that a Rule 60(b) reinstatement would be granted as a routine matter after a voluntary dismissal, and for that reason they made no attempt to demonstrate that exceptional circumstances warranted relief from the dismissal. This was simply a mistake, and a court is not obliged to grant relief from a lawyer's mistaken reading of a rule or statute. Eskridge, 577 F.3d at 810; Webb v. James, 147 F.3d 617, 622 (7th Cir.1998).
Counsel conceded at oral argument that he assumed that Rule 60(b) operates the same way as the Illinois statute governing voluntary dismissals. See 735 ILCS 5/13-217. That provision specifies that if a plaintiff voluntarily dismisses an action, the plaintiff "may commence a new action within one year or within the remaining period of limitation, whichever is greater[.]" 735 ILCS 5/13-217. There is no such safe harbor in the federal rules, although in federal cases governed by Illinois' statute of limitations, we will apply the coordinate tolling rule set forth in Section 5/13-217. Jenkins, 506 F.3d at 623-24. The instant case is governed by a federal statute of limitations, however, so that exception does not help the plaintiffs here. In federal cases, the limitations period continues to run after the case is dismissed without prejudice. Lee v. Cook County, Ill., 635 F.3d 969, 971-72 (7th Cir.2011). As counsel acknowledged at oral argument, he should have moved to stay proceedings pending the outcome of the criminal case. He did not do so because he did not wish to reveal to the court or to his opponent the reason for the stay. This was a tactical decision based on a mistaken reading of Rule 60. "An inadvertent `mistake' that might justify relief typically involves a misunderstanding of the surrounding facts and circumstances." Eskridge, 577 F.3d at 809. Counsel here simply misunderstood the applicable rule of civil procedure. It is well within a *591 district court's discretion to determine whether this kind of mistake or neglect was excusable. Webb, 147 F.3d at 622. See also Cash v. Illinois Div. of Mental Health, 209 F.3d 695, 697-98 (7th Cir. 2000) (Rule 60(b) is not intended to correct mere legal blunders). The district court declined to relieve the plaintiffs of the consequences of their tactical decision to voluntarily dismiss. A court abuses its discretion only when no reasonable person could agree with the decision to deny relief. Eskridge, 577 F.3d at 809. There is no abuse of discretion here.
AFFIRMED.
NOTES
[1]  The original complaint named several individual defendants in addition to DHS. A few months after filing, the plaintiffs amended the complaint to remove the individual defendants and to substitute Ernest Carter for one of the original plaintiffs, Michael Verre.
