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Long-term Debt - Additional Information (Details) - USD ($) $ in Millions					3 Months Ended		9 Months Ended		12 Months Ended
	Jul. 06, 2022	Apr. 01, 2021	Jun. 12, 2020	Feb. 14, 2020	Sep. 30, 2022	Jun. 30, 2021	Sep. 30, 2022	Sep. 30, 2021	Dec. 31, 2021
Debt Instrument [Line Items]
Debt instrument, description							On April 1, 2021, the Company completed a private offering of Senior Secured Second Lien Notes (the “Notes”), for the purposes of, among other things, repayment and refinancing of a portion of the Company’s prior existing debt, reducing interest rate exposure and providing liquidity for financing of future growth initiatives.
Outstanding borrowing					$ 158.4		$ 158.4		$ 100.7
Loss on extinguishment of debt						$ 11.9		$ 11.9
Imputed interest							0.2	$ 0.2
PeakLogix \| Non-Contingent Consideration
Debt Instrument [Line Items]
Imputed interest paid					0.8
Term Loan
Debt Instrument [Line Items]
Debt instrument, face amount				$ 155.0
Debt instrument, maturity period				2025-08
Payable in monthly installments							$ 1.9
Repayment of outstanding loan		$ 147.3
Term Loan \| SOFR Plus
Debt Instrument [Line Items]
Debt Instrument, variable rate							8.00%
Notes Payable \| PeakLogix \| Non-Contingent Consideration
Debt Instrument [Line Items]
Earn-out payment period			5 years
Amount of minimum cash payments using a market participant discount rate							$ 1.0
Imputed interest							0.1
Notes Payable \| PeakLogix \| Non-Contingent Consideration \| Other Liabilities
Debt Instrument [Line Items]
Present value of non-contingent earn-out liability							1.1		1.8
5.625% Senior Secured Second Lien Notes due 2026
Debt Instrument [Line Items]
Proceeds from sale of notes		$ 315.0
Debt instrument, interest rate		5.625%
Notes maturity date		Apr. 15, 2026
Outstanding borrowing					310.8		310.8
Original issue discount and deferred financing costs					$ 4.2		$ 4.2
Effective interest rate					5.93%		5.93%
Minimum \| Notes Payable \| PeakLogix \| Non-Contingent Consideration
Debt Instrument [Line Items]
Additional earn-out payment			$ 2.0
ABL Facility
Debt Instrument [Line Items]
Outstanding borrowing					$ 158.4		$ 158.4		$ 100.7
Effective interest rate					5.00%		5.00%		2.30%
ABL Facility \| Yale Industrial Trucks Inc.
Debt Instrument [Line Items]
Business combination stock exercised value	$ 80.0
Business combination stock acquired value	150.0
ABL Facility \| Minimum \| Yale Industrial Trucks Inc.
Debt Instrument [Line Items]
Maximum borrowing capacity	350.0
ABL Facility \| Maximum \| Yale Industrial Trucks Inc.
Debt Instrument [Line Items]
Maximum borrowing capacity	430.0
ABL Facility \| Canadian-denominated Sublimit Facility \| Yale Industrial Trucks Inc.
Debt Instrument [Line Items]
Maximum borrowing capacity	$ 35.0
First Lien Lender \| Floor Plans and ABL Facility
Debt Instrument [Line Items]
Maximum borrowing capacity					$ 780.0		$ 780.0
Outstanding borrowing					368.8		368.8		$ 255.6
Original issue discount and deferred financing costs					$ 2.3		$ 2.3		$ 2.4